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Combining the Liouville equations for polar motion (PM) with forecasted geophysical effective angular momentum (EAM) functions can significantly improve the accuracy of Earth's PM predictions. These predictions rely on deconvolution and convolution methods. Deconvolution derives the geodetic EAM function from the PM observations, while convolution uses both the geodetic and geophysical EAM functions to reproduce and predict the PM values. However, there are limitations in existing numerical realisations of deconvolution and convolution that must be addressed. These limitations include low-frequency biases, high-frequency errors, and edge errors, which can negatively impact the accuracy of PM prediction. To overcome these concerns, we develop the Convolution Least Squares (Conv-LS) scheme through a multi-perspective analysis in the frequency domain, PM domain, and EAM domain. By comparing representative approaches for reproducing three different PM series (IERS C01, IERS C04, and IGS) with varying sampling intervals (18.25 days, daily, and 6 h), we demonstrate that the Conv-LS scheme can effectively eliminate the usually present spurious signals and also integrate high-accuracy deconvolution algorithms to reduce reproduced errors further. Compared to the traditional approacsh (using a low-accuracy discrete PM equation for deconvolution and numerical integration for convolution), our new approach (utilising a high-accuracy deconvolution algorithm along with the Conv-LS scheme for convolution) reduces the standard deviations of the residuals' x-component by 31.0%, 60.1%, and 13.7% for C01, C04, and IGS PM series, respectively, while also reducing the y-component by 17.3%, 47.0%, and 14.0%, respectively. These results highlight the superiority of the Conv-LS scheme, leading us to recommend it for practical applications. [ABSTRACT FROM AUTHOR]

Recently, a regularized Kaczmarz method has been proposed to solve tensor recovery problems. In this article, we propose a sampling greedy average regularized Kaczmarz method. This method can be viewed as a block or mini‐batch version of the regularized Kaczmarz method, which is based on averaging several regularized Kaczmarz steps with a constant or adaptive extrapolated step size. Also, it is equipped with a sampling greedy strategy to select the working tensor slices from the sensing tensor. We prove that our new method converges linearly in expectation and show that the sampling greedy strategy can exhibit an accelerated convergence rate compared to the random sampling strategy. Numerical experiments are carried out to show the feasibility and efficiency of our new method on various signal/image recovery problems, including sparse signal recovery, image inpainting, and image deconvolution. [ABSTRACT FROM AUTHOR]

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This review analyzes a development in biochemistry, enzymology and biotechnology that originally came as a surprise. Following the establishment of directed evolution of stereoselective enzymes in organic chemistry, the concept of partial or complete deconvolution of selective multi‐mutational variants was introduced. Early deconvolution experiments of stereoselective variants led to the finding that mutations can interact cooperatively or antagonistically with one another, not just additively. During the past decade, this phenomenon was shown to be general. In some studies, molecular dynamics (MD) and quantum mechanics/molecular mechanics (QM/MM) computations were performed in order to shed light on the origin of non‐additivity at all stages of an evolutionary upward climb. Data of complete deconvolution can be used to construct unique multi‐dimensional rugged fitness pathway landscapes, which provide mechanistic insights different from traditional fitness landscapes. Along a related line, biochemists have long tested the result of introducing two point mutations in an enzyme for mechanistic reasons, followed by a comparison of the respective double mutant in so‐called double mutant cycles, which originally showed only additive effects, but more recently also uncovered cooperative and antagonistic non‐additive effects. We conclude with suggestions for future work, and call for a unified overall picture of non‐additivity and epistasis. [ABSTRACT FROM AUTHOR]

This article addresses the deconvolution problem of estimating a square-integrable probability density from observations contaminated with additive measurement errors having a known density. The estimator begins with a density estimate of the contaminated observations and minimizes a reconstruction error penalized by an integrated squared mth derivative. Theory for deconvolution has mainly focused on kernel- or wavelet-based techniques, but other methods including spline-based techniques and this smoothness-penalized estimator have been found to outperform kernel methods in simulation studies. This article fills in some of these gaps by establishing asymptotic guarantees for the smoothness-penalized approach. Consistency is established in mean integrated squared error, and rates of convergence are derived for Gaussian, Cauchy, and Laplace error densities, attaining some lower bounds already in the literature. The assumptions are weak for most results; the estimator can be used with a broader class of error densities than the deconvoluting kernel. Our application example estimates the density of the mean cytotoxicity of certain bacterial isolates under random sampling; this mean cytotoxicity can only be measured experimentally with additive error, leading to the deconvolution problem. We also describe a method for approximating the solution by a cubic spline, which reduces to a quadratic program. for this article are available online. [ABSTRACT FROM AUTHOR]

The authors present a new algorithm for analyzing ray deflection within spherical refractive index fields. The algorithm emanates from the well-known deconvolution algorithm for axisymmetric refractive index fields using the inverse Abel transformation and can be used for experimental Rainbow Schlieren Deflectometry (RSD) data. It was numerically validated by Computational Fluid Dynamics (CFD) calculations of free convection around an isothermal sphere and successive ray tracing through the determined temperature field. The algorithm determined radial temperature profiles and local Nusselt numbers from resulting deflection angles of the ray tracing simulations. An excellent agreement between original and reconstructed temperature field within the limits of assumptions was reached. This proves the usability of the algorithm for the experimental determination of spherical refractive index fields from future heat or mass transfer experiments. [ABSTRACT FROM AUTHOR]

Too much reliance has been placed on calculating single images meeting possibly arbitrary optimization criteria. By generating a dispersion of multiple images consistent with the data, we may be able to learn how wrong we could be. Our problem is to generate a way of seeing a representative sample of all of the solutions in the hyperplane of solutions, which would be an array of images, each of which is a solution to the equations. To accomplish this, we suggest that our sampling is in a space of image basis functions, rather than directly in the hyperplane. As the number of basis functions is large, we design a selection criterion for choosing a subset that reasonably spans the space of images. First, we try a random sampling, which gives high frequency or sequency samples. Then we turn to more systematic sampling, based on the methods developed for one-pixel imaging. Some numerical experiments demonstrate that the use of basis functions as starting images for ART-like iterative algorithms may suffice to span the hyperplane of solutions, allowing choices between solutions other than simple optimization of arbitrary criteria such as minimum norm or maximum entropy, or deconvolution of the point spread function of the algorithm. [ABSTRACT FROM AUTHOR]

When time-domain TPA methods used for tackling vibrations and noise problems in omplex systems during transient conditions, which failed to overcome the ill-conditioned problems of he frequency response functions matrix near natural frequencies, and showed low accuracy in extrac¬ing the required time-domain information from the existing frequency-domain data. Therefore, a new time-domain TPA method was developed based on AKF. This method started with estimating time-domain operational loads using AKF supplemented by GA, and then identified the impulse response unctions using LS algorithm. Finally, time-domain contributions for each transfer path was computed by linearly convolving time-domain operational loads with respective impulse response functions. Case tudy demonstrates that the load-identification errors of AKF applied in the proposed method are smaller than that of traditional deconvolution filters. Additionally, the errors of impulse response unctions identified by LS algorithm are smaller than those obtained by direct inverse fast Fourier ransform or creating finite impulse response filters from frequency response functions. Furthermore, he proposed method achieves small errors even in complex structures. [ABSTRACT FROM AUTHOR]

This paper presents an integrated approach involving geophysical and remote sensing datasets in the identification of regions that have undergone hydrothermal alteration in the gold-hosted site of the Ife–Ilesa schist belt. Geophysical methods employed include the aeromagnetic and aeroradiometric data, while the remote sensing involved Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) data. Derivatives such as analytic signal, total horizontal derivative, tilt derivative of the total horizontal derivative, and 3-D Euler deconvolution were applied on the aeromagnetic data for the mapping and delineation of structures guiding migration of hydrothermal and mineralizing fluids in the study area. Radiometric analyses involving K/eTh, Ideal K anomalies deviation (Kd), and F-parameter, including principal component analyses on ASTER to isolate Potassic, Argillic, Propylitic, and Phyllic alteration zones were performed to delineate hydrothermally altered zones. The lineament map showed that the study area is geodynamically active as evident by the presence of deep-seated intersecting structures with depths ranging from 189 to 899 m, principally trending NE–SW, which is an impression of the Pan–African orogeny. The fuzzy gamma operator 0.9 was thereafter used in the integration of aeroradiometric and ASTER data for the hydrothermal alteration map production. Subsequently, five classes ranging from background to very high alteration anomalies were derived using the concentration–area (C–A) fractal model from the hydrothermal alteration map. These classes reveal the pervasive styles of alteration in the study area. The study further revealed the close association of structures, granitoids, hydrothermal alteration, and orogenic gold deposits. Also, the flurry of mining activities in the southern flank of the study coincides with most of the hydrothermally mapped areas with the Prediction–area (P–A) plot showing 78% occurrence of orogenic gold deposits in 22% of the total area explored. This translates to high potential of orogenic gold mineralization in the study area. The study therefore concluded based on the validation result that hydrothermal alteration mapping is important in the mapping of orogenic gold deposit. Hence, unexplored areas particularly in the western and eastern flank of the study area where there are strong indications of hydrothermal alteration have good prospect for gold mineralization. [ABSTRACT FROM AUTHOR]

A lensless holographic microscope based on in-line holograms and optical diffraction tomography is an ideal imaging system for label-free 3D biological samples and can achieve large-volume imaging with single-cell resolution in a convenient way. However, due to the phase information loss and the missing cone problem, the imaging quality is significantly degraded by the reconstructed artifacts of twin images and out-of-focus images, which severely hinders the identification and interpretation of the objects. We propose an artifacts-free lensless on-chip tomography certified by three-dimensional deconvolution, which facilitates the extraction of real object morphology through straightforward yet effective computation. Initially, a globally valid systemic point spread function (PSF) is generated by simulating the imaging output of an ideal point light source positioned at the origin of the object space coordinate. Subsequently, an iterative three-dimensional deconvolution process is applied to the primitive imaging outcome of the lensless on-chip tomography using this PSF. Through rapid iterations, the optimized imaging result is swiftly obtained. Both the simulated and experimental results indicate that the artifacts-free lensless on-chip tomography can effectively circumvent the reconstructed artifacts and retrieve the real object morphology, which is critical for detailed observation and further quantitative analysis. In addition, we anticipate that the proposed approach has the potential to be transferred to other 3D imaging systems in systemic artifacts removal after corresponding modifications. [ABSTRACT FROM AUTHOR]

In many areas, such as speech processing, communication, and measurement systems, where the actual signal is not directly available, Wiener deconvolution is a widely used signal restoration technique. The accuracy of the estimated signal in Wiener deconvolution is determined by the unknown filter parameter. To compute this unknown parameter, complex and time-consuming numerical as well as iterative computation approaches were proposed in the literature, which also often compute an unoptimized unknown filter parameter. To address the computational problem and estimate a more accurate unknown filter parameter, the authors reported an analytical solution in a prior work for a given signal to noise ratio. However, it was revealed that the actual optimum parameter value also varies with noise also. In this paper, the authors propose a new analytical solution for optimum parameter estimation that includes noise as well. The authors compared the modified analytical solution to existing numerical computation methods for different values of Signal to Noise Ratio and demonstrated that the proposed methods' optimum parameter estimation is always close to the actual optimum value, which resulted in more accurate signal deconvolution. Proposed mathematical solutions are also verified with experimental signals, acquired in a laboratory. [ABSTRACT FROM AUTHOR]

An editorial focuses on advancing seismic data reconstruction methods through the integration of anti-aliasing techniques with vector Projection onto Convex Sets (POCS) methods. It introduces an enhanced approach to reconstruct multicomponent seismic data, addressing the limitations of existing methods that often reconstruct each component independently and lack anti-aliasing mechanisms.

In order to overcome the defects that the analysis of multi-well typical curves of shale gas reservoirs is rarely applied to engineering, this study proposes a robust production data analysis method based on deconvolution, which is used for multi-well inter-well interference research. In this study, a multi-well conceptual trilinear seepage model for multi-stage fractured horizontal wells was established, and its Laplace solutions under two different outer boundary conditions were obtained. Then, an improved pressure deconvolution algorithm was used to normalize the scattered production data. Furthermore, the typical curve fitting was carried out using the production data and the seepage model solution. Finally, some reservoir parameters and fracturing parameters were interpreted, and the intensity of inter-well interference was compared. The effectiveness of the method was verified by analyzing the production dynamic data of six shale gas wells in Duvernay area. The results showed that the fitting effect of typical curves was greatly improved due to the mutual restriction between deconvolution calculation parameter debugging and seepage model parameter debugging. Besides, by using the morphological characteristics of the log-log typical curves and the time corresponding to the intersection point of the log-log typical curves of two models under different outer boundary conditions, the strength of the interference between wells on the same well platform was well judged. This work can provide a reference for the optimization of well spacing and hydraulic fracturing measures for shale gas wells. [ABSTRACT FROM AUTHOR]

Me 2-1 is a high-excitation planetary nebula whose morphology and physical structure have not yet been investigated. We present narrow-band images in several emission lines, and high- and intermediate-resolution long-slit spectra aimed at investigating its morphology and 3D structure, and its physical parameters and chemical abundances. By applying deconvolution techniques to the images, we identified in Me 2-1: an elliptical ring; two elongated, curved structures (caps) that contain three pairs of bright point-symmetric (PS) knots; a shell interior of the ring; and a faint halo or attached shell. The caps are observed in all images, while the PS knots are only observed in the low-excitation emission line ones. These structures are also identified in the high-resolution long-slit spectra, allowing us to study their morphokinematics. The 3D reconstruction shows that Me 2-1 consists of a ring seen almost pole-on, and a virtually spherical shell, to which the caps and PS knots are attached. Caps and PS knots most probably trace the sites where high-velocity collimated bipolar outflows, ejected along a wobbling axis, collide with the spherical shell, are slowed down, and remain attached to it. Although the main excitation mechanism in Me 2-1 is found to be photoionization, a contribution of shocks in the PS knots is suggested by their emission line ratios. The combination of collimated outflows and a ring with a spherical shell is unusual among planetary nebulae. We speculate that two planets, each with less than one Jupiter mass, could be involved in the formation of Me 2-1 if both enter a common envelope evolution during the asymptotic giant branch phase of the progenitor. One planet is tidally disrupted, forming an accretion disk around the central star, from which collimated bipolar outflows are ejected; the other planet survives, causing wobbling of the accretion disk. The physical parameters and chemical abundances obtained from our intermediate-resolution spectrum are similar to those obtained in previous analyses, with the abundances also pointing to a low-mass progenitor of Me 2-1. [ABSTRACT FROM AUTHOR]

Summary Computational cell-type deconvolution is an important analytic technique for modeling the compositional heterogeneity of bulk gene expression data. A conceptually new Bayesian approach to this problem, BayesPrism, has recently been proposed and has subsequently been shown to be superior in accuracy and robustness against model misspecifications by independent studies; however, given that BayesPrism relies on Gibbs sampling, it is orders of magnitude more computationally expensive than standard approaches. Here, we introduce the InstaPrism package which re-implements BayesPrism in a derandomized framework by replacing the time-consuming Gibbs sampling step with a fixed-point algorithm. We demonstrate that the new algorithm is effectively equivalent to BayesPrism while providing a considerable speed and memory advantage. Furthermore, the InstaPrism package is equipped with a precompiled, curated set of references tailored for a variety of cancer types, streamlining the deconvolution process. Availability and implementation The package InstaPrism is freely available at: https://github.com/humengying0907/InstaPrism. The source code and evaluation pipeline used in this paper can be found at: https://github.com/humengying0907/InstaPrismSourceCode. [ABSTRACT FROM AUTHOR]

The purpose of this study was to develop an in vitro release testing (IVRT) strategy to predict the pre-clinical performance of single agent and combination long acting injectable (LAI) suspension products. Two accelerated IVRT methods were developed using USP apparatus 2 to characterize initial, intermediate, and terminal phases of drug release. Initial and intermediate phases were captured using a suspension cup with moderate agitation to ensure a constant, low surface area exposure of the LAI suspension to the release media. The terminal phase was obtained by exposing the LAI suspension to a high initial paddle speed. This resulted in smaller suspension particulates with high cumulative surface area that were dispersed throughout the release media, enabling rapid drug release. The in vitro release profiles obtained with these two methods in 48 h or less were independently time scaled to reflect the in vivo time scale of approximately 1800 h. Level-A in vitro in vivo correlations (IVIVCs) were separately developed for each method and active pharmaceutical ingredient (API) using in vivo absorption profiles obtained by deconvolution of rat plasma concentration-time profiles. The IVIVCs were successfully validated for each API. This work provides a framework for evaluating individual phases of drug release of complex LAIs to ultimately predict their in vivo performance. [Display omitted] • Two in vitro release testing (IVRT) methods using USP Apparatus-2 comprised the accelerated and biopredictive IVRT strategy. • The methods were accelerated to different extents to characterize the initial and later phases of drug release from LAIs. • The in vitro release profiles obtained in 48 hours or less were time scaled to reflect the in vivo time scale of 75 days. • In vitro in vivo correlations were developed and validated for each active using preclinical rat data. [ABSTRACT FROM AUTHOR]

Carbonaceous material (CM) undergoes progressive changes that reflect its thermal history. These changes are in general irreversible and provide valuable information for understanding diagenetic and metamorphic processes of crustal rocks. Among various approaches to quantify these changes, the R2 ratio, area ratio of specific peaks in CM Raman spectra, is widely used to estimate the maximum temperature of intermediate- to moderately high-grade metamorphism. The calculation of the R2 ratio requires peak deconvolution of the original spectrum, and the results depend on the details of how this is carried out. However, a clear protocol for selecting appropriate initial conditions has not been established and obtaining a reliable temperature estimate depends at least in part on the experience and skill of the operator. In this study, we developed a Python code that automatically calculates the R2 ratio from CM Raman spectra. Our code produces R2 ratios that are generally in good agreement with those of Aoya et al. (J Metamorph Geol 28:895–914, 2010, https://doi.org/10.1111/j.1525-1314.2010.00896.x) for the same Raman data, with much less time and effort than was the case in the previous studies. We have confirmed that the code is also applicable to other previous datasets from both contact and regional metamorphic regions. The overall trend of the recalculated data indicates that samples with R2 greater than ~ 0.7 are not sensitive to the changes in CM maturity and thus should not be used for the calibration of an R2-based geothermometer. We propose a modified geothermometer for contact metamorphism that is strictly applicable to samples with R2 from 0.023 to 0.516, with the proviso that a laser with a wavelength of 532 nm should be used. A slight extrapolation of the newly proposed geothermometer up to R2 of 0.57 provides a temperature estimate that is consistent with the geothermometer of Kaneki and Kouketsu (Island Arc 31:e12467, 2022; https://doi.org/10.1111/iar.12467); the boundary between the two geothermometers corresponds to a temperature of 391 °C. [ABSTRACT FROM AUTHOR]

Seismic deconvolution is a useful tool in seismic data processing. Classical non-machine learning deconvolution methods usually apply quite a few constraints to both wavelet inversion and reflectivity inversion. Supervised machine learning deconvolution methods often require appropriate training labels. The existing self-supervised machine learning deconvolution methods need a given wavelet, which is a non-blind process. To overcome these issues, we propose a blind deconvolution method based on self-supervised machine learning. This method first estimates an initial zero-phase wavelet by smoothing the amplitude spectrum of averaged seismic data. Then, the loss function of self-supervised machine learning is taken as the error between the observed seismic data and the reconstructed seismic data that come from the convolution of phase-rotated wavelet and reflectivity generated by the network. We utilize a residual neural network with long skip connections as the reflectivity inversion network and a fully connected convolutional neural network as the wavelet phase inversion network. Numerical experiments on synthetic data and field data show that the proposed method can obtain reflectivity inversion results with higher resolution than the existing self-supervised machine learning method without given wavelet. [ABSTRACT FROM AUTHOR]

When scanning a document printed on both sides by using an electronic scanner, the printed material on the back (front) side may be transmitted to the front (back) side. This phenomenon is called show-through. The problem to remove the show-through from scanned images is called the show-through removal in the literature. In this paper, we propose a new method of show-through removal based on the following principle. The proposed method uses two scanned images with the front side and with the back side as input images. The proposed method is based on Ahmed's Blind Image Deconvolution method discovered in 2013, which succeeded in formulating Blind Image Deconvolution as a nuclear norm minimization. Since the structure of show-through removal resembles that of Blind Image Deconvolution, we discovered that the show-through removal can be reformulated into a nuclear norm minimization in the space of outer product matrix constructed from an image vector and a point spread function vector of blurring. Using this key idea, we constructed the proposed method as follows. First, our cost function consists of the following three terms. The first term is the data term and the second term is the nuclear norm derived from the above reformulation. The third term is a regularization term to overcome the underdetermined nature of show-through removal problem and the existence of noise in the measured images. The regularization term consists of Total Variation imposed on the images. The resulting nuclear norm minimization problem is solved by using Accelerated Proximal Gradient method and Singular Value Projection with some problem-specific modifications, which converges fast and requires a simple implementation. We show results of simulation studies as well as results of real image experiments to demonstrate the performances of the proposed method. [ABSTRACT FROM AUTHOR]

The estimation of auditory evoked potentials requires deconvolution when the duration of the responses to be recovered exceeds the inter-stimulus interval. Based on least squares deconvolution, in this article we extend the procedure to the case of a multi-response convolutional model, that is, a model in which different categories of stimulus are expected to evoke different responses. The computational cost of the multi-response deconvolution significantly increases with the number of responses to be deconvolved, which restricts its applicability in practical situations. In order to alleviate this restriction, we propose to perform the multi-response deconvolution in a reduced representation space associated with a latency-dependent filtering of auditory responses, which provides a significant dimensionality reduction. We demonstrate the practical viability of the multi-response deconvolution with auditory responses evoked by clicks presented at different levels and categorized according to their stimulation level. The multi-response deconvolution applied in a reduced representation space provides the least squares estimation of the responses with a reasonable computational load. matlab/Octave code implementing the proposed procedure is included as supplementary material. [ABSTRACT FROM AUTHOR]

Improving the resolution of seismic migration images plays an important role for geophysical interpreters to characterize underground reservoirs. However, the classical image domain least‐squares migration method based on the local‐stationary assumption cannot obtain a satisfactory high‐resolution seismic image due to the significant spatial variant characteristics of the point spread function. To mitigate this problem, we proposed a high‐resolution point spread function deconvolution method and applied it to two‐dimensional cases. Nevertheless, extending the two‐dimensional method to three‐dimensional problems directly would fail due to the intrinsic complexity in three‐dimensional cases. In this study, we resolve the differences encountered in the point spread function deconvolution method for two‐ and three‐dimensional cases and provide specific strategies for achieving high‐resolution imaging with low computational cost when extending the point spread function deconvolution method to three‐dimensional cases. The main schemes include (1) incorporating the analytical expression of the point spread function to guide the generation of three‐dimensional point spread function distributions, (2) extending the point spread function filter calculation method from a two‐dimensional square to a three‐dimensional rectangular prism and (3) interpolating to obtain more compact point spread functions for reducing migration artefacts. Results from the three‐dimensional synthetic Overthrust model and field data set demonstrate that our techniques could effectively enhance the spatial resolution of the migration images with reduced migration artefacts. With these specific strategies, the space‐variant point spread function deconvolution algorithm shows superior performance on three‐dimensional cases at a much lower computational cost compared with the classical least‐squares migration method and the local‐stationary deblurring method. Synthetic tests and real data applications confirm that the space‐variant point spread function deconvolution method has distinct advantages over both two‐ and three‐dimensional problems and can be widely adopted in practice. [ABSTRACT FROM AUTHOR]

The Euler deconvolution system is a well-known approach to estimate the depth of underground sources in potential field geophysics. Overdetermined Euler linear equations are usually solved independently and separately for the gravity and magnetic data, and each result is an estimate for the depth of the potential sources. This technique is widely utilized to analyze the depth variations of magnetic and gravity sources individually. However, the depth estimation of each of the mentioned potential fields may return specific and exclusive results regarding the complex nature of the subsurface structures, and the gravity and magnetic separate depth estimation solutions may be discordant in many aspects. In the cases of low-resolution for the gravity and magnetic data sets, this study indicates that the independently solved Euler depth estimation systems cannot yield reliable and accurate solutions for potential field sources. By combining the gravity and magnetic data and simultaneously solving the Euler equations for the gravity and magnetic potential fields, this research presents a novel approach called the joint Euler method with a proper capability to return more accurate and improved depth estimations for the boundary and body of potential field sources. The presented method was solved and examined over homogeneous and non-homogeneous synthetic scenarios with reduced resolution, and the depth solutions were also compared with the separate approach. After obtaining the desired results from the synthetic models, the joint Euler technique was applied to the gravity and magnetic data of the Kifl oil trap located in Iraq. The results were quite promising compared to the separate depth estimations, proving the sufficiency and applicability of the proposed potential field method in terms of interpretational aspects. [ABSTRACT FROM AUTHOR]

In ground-based astronomical observations or artificial space target detections, images obtained from a ground-based telescope are severely distorted due to atmospheric turbulence. The distortion can be partially compensated by employing adaptive optics (pre-detection compensation), image restoration techniques (post-detection compensation), or a combination of both (hybrid compensation). This paper focuses on the improvement of the most commonly used practical post-processing techniques, Richardson–Lucy (R–L) iteration blind deconvolution, which is studied in detail and improved as follows: First, the total variation (TV) norm is redefined using the Gaussian gradient magnitude and a set scheme for regularization parameter selection is proposed. Second, the Gaussian TV constraint is proposed to impose to the R–L algorithm. Last, the Gaussian TV R–L (GRL) iterative blind deconvolution method is finally presented, in which the restoration precision is visually increased and the convergence property is considerably improved. The performance of the proposed GRL method is tested by both simulation experiments and observed field data. [ABSTRACT FROM AUTHOR]

Efficiently mapping of cell types in situ remains a major challenge in spatial transcriptomics. Most spot deconvolution tools ignore spatial coordinate information and perform extremely slow on large datasets. Here, we introduce SpatialPrompt, a spatially aware and scalable tool for spot deconvolution and domain identification. SpatialPrompt integrates gene expression, spatial location, and single-cell RNA sequencing (scRNA-seq) dataset as reference to accurately infer cell-type proportions of spatial spots. SpatialPrompt uses non-negative ridge regression and graph neural network to efficiently capture local microenvironment information. Our extensive benchmarking analysis on Visium, Slide-seq, and MERFISH datasets demonstrated superior performance of SpatialPrompt over 15 existing tools. On mouse hippocampus dataset, SpatialPrompt achieves spot deconvolution and domain identification within 2 minutes for 50,000 spots. Overall, domain identification using SpatialPrompt was 44 to 150 times faster than existing methods. We build a database housing 40 plus curated scRNA-seq datasets for seamless integration with SpatialPrompt for spot deconvolution. The authors present SpatialPrompt, a tool that offers high accuracy and scalability for spot deconvolution and domain identification in spatial transcriptomics, showing superior performance on diverse spatial datasets. [ABSTRACT FROM AUTHOR]

Spatial transcriptomics (ST) technologies allow the profiling of the transcriptome of cells while keeping their spatial context. Since most commercial untargeted ST technologies do not yet operate at single-cell resolution, computational methods such as deconvolution are often used to infer the cell type composition of each sequenced spot. We benchmarked 11 deconvolution methods using 63 silver standards, 3 gold standards, and 2 case studies on liver and melanoma tissues. We developed a simulation engine called synthspot to generate silver standards from single-cell RNA-sequencing data, while gold standards are generated by pooling single cells from targeted ST data. We evaluated methods based on their performance, stability across different reference datasets, and scalability. We found that cell2location and RCTD are the top-performing methods, but surprisingly, a simple regression model outperforms almost half of the dedicated spatial deconvolution methods. Furthermore, we observe that the performance of all methods significantly decreased in datasets with highly abundant or rare cell types. Our results are reproducible in a Next-flow pipeline, which also allows users to generate synthetic data, run deconvolution methods and optionally benchmark them on their dataset (https://github.com/saeyslab/spotless-benchmark). [ABSTRACT FROM AUTHOR]

Image production tools do not always create a clear image, noisy and blurry images are sometimes created. Among these cases, Poissonian noise is one of the most famous noises that appear in medical images and images taken in astronomy. In recent years, various methods have been proposed to improve the quality of the image that has been lost due to this noise. For example, we can refer to methods that use fractional-order and second-order total variation priors or proximal thresholding. In this paper, in the first step, based on framelet transform, a local minimal prior is introduced, and in the next step, this tool together with fractional calculation is used for Poissonian blurred image deconvolution. The framelet transform domain of images usually have sparse representations. It is also well known that the use of framelet transfer has a proper effect on the edges of the restored image. Also, In this study, both blind and nonblind problems are considered. To evaluate the performance of the presented model, several images such as real images have been investigated. Various tools are used to study the efficiency of the proposed method such as PSNR and SSIM. The proposed method is compared with the existing methods such as fractional - order and second-order total variation. The simulation results show the appropriate representation of the proposed method in solving this type of problem. [ABSTRACT FROM AUTHOR]

The proposed work focuses on a new set of robust H ∞ deconvolution filtering of 3-D objects using feature extraction from Orthogonal Descriptor such as Racah moment, and Roesser local state-space model with uncertain parameters. The time-invariant uncertain parameters are supposed to belong to a polytope with known vertices. The main idea is to design robust H ∞ deconvolution filter to reconstruct the noisy 3D object from the feature extractions of Racah moments. Furthermore, the filtering error system is asymptotically stable and satisfies the H ∞ performance index for all admissible uncertainties. The sufficient condition is given to ensure the H ∞ performance of the filtering error system through the parameter-dependent linear matrix inequalities (LMIs) constraints, and the Racah moment to give the feature extraction according to the order defined in advance instead of the global 3-D object. Moreover, the robust 3-D deconvolution filter is designed to achieve the H ∞ performance index which the robust filter parameters are determined with certain optimization resolution. Finally, simulation result is shown to demonstrate the usefulness of the suggested design approach. [ABSTRACT FROM AUTHOR]

Simple Summary: Fish fry counting finds applications in various scenarios, including fish fry trading and the management of breeding densities. However, current computer-based methods struggle to accurately and effectively count large numbers of fish fry and locate them. To address these challenges, this study proposes a fish fry counting method based on a single keypoint as a feature. Additionally, a large-scale fish fry dataset, FishFry-2023, has been constructed, which includes universal point annotations for use. The number of fry in a single image ranges from 204 to 1935, ensuring an effective evaluation of the proposed method. Our approach was trained and tested on FishFry-2023, with experimental results demonstrating an average counting accuracy of 98.59%, exhibiting higher counting precision compared to the density map algorithms now available. Fish fry counting has been vital in fish farming, but current computer-based methods are not feasible enough to accurately and efficiently calculate large number of fry in a single count due to severe occlusion, dense distribution and the small size of fish fry. To address this problem, we propose the deconvolution enhancement keypoint network (DEKNet), a method for fish fry counting that features a single-keypoint approach. This novel approach models the fish fry as a point located in the central part of the fish head, laying the foundation for our innovative counting strategy. To be specific, first, a fish fry feature extractor (FFE) characterized by parallel dual branches is designed for high-resolution representation. Next, two identical deconvolution modules (TDMs) are added to the generation head for a high-quality and high-resolution keypoint heatmap with the same resolution size as the input image, thus facilitating the precise counting of fish fry. Then, the local peak value of the heatmap is obtained as the keypoint of the fish fry, so the number of these keypoints with coordinate information equals the number of fry, and the coordinates of the keypoint can be used to locate the fry. Finally, FishFry-2023, a large-scale fish fry dataset, is constructed to evaluate the effectiveness of the method proposed by us. Experimental results show that an accuracy rate of 98.59% was accomplished in fish fry counting. Furthermore, DEKNet achieved a high degree of accuracy on the Penaeus dataset (98.51%) and an MAE of 13.32 on a public dataset known as Adipocyte Cells. The research outcomes reveal that DEKNet has superior comprehensive performance in counting accuracy, the number of parameters and computational effort. [ABSTRACT FROM AUTHOR]

Spatial transcriptomics (ST) data have emerged as a pivotal approach to comprehending the function and interplay of cells within intricate tissues. Nonetheless, analyses of ST data are restricted by the low spatial resolution and limited number of ribonucleic acid transcripts that can be detected with several popular ST techniques. In this study, we propose that both of the above issues can be significantly improved by introducing a deep graph co-embedding framework. First, we establish a self-supervised, co-graph convolution network–based deep learning model termed SpatialcoGCN, which leverages single-cell data to deconvolve the cell mixtures in spatial data. Evaluations of SpatialcoGCN on a series of simulated ST data and real ST datasets from human ductal carcinoma in situ , developing human heart and mouse brain suggest that SpatialcoGCN could outperform other state-of-the-art cell type deconvolution methods in estimating per-spot cell composition. Moreover, with competitive accuracy, SpatialcoGCN could also recover the spatial distribution of transcripts that are not detected by raw ST data. With a similar co-embedding framework, we further established a spatial information–aware ST data simulation method, SpatialcoGCN-Sim. SpatialcoGCN-Sim could generate simulated ST data with high similarity to real datasets. Together, our approaches provide efficient tools for studying the spatial organization of heterogeneous cells within complex tissues. [ABSTRACT FROM AUTHOR]

Ocean Acoustic Waveguide Remote Sensing (OAWRS) typically utilizes large-aperture linear arrays combined with coherent beamforming to estimate the spatial distribution of acoustic scattering echoes. The conventional maximum likelihood deconvolution (DCV) method uses a likelihood model that is inaccurate in the presence of multiple adjacent targets with significant intensity differences. In this study, we propose a deconvolution algorithm based on a modified likelihood model of beamformed intensities (M-DCV) for estimation of the spatial intensity distribution. The simulated annealing iterative scheme is used to obtain the maximum likelihood estimation. An approximate expression based on the generalized negative binomial (GNB) distribution is introduced to calculate the conditional probability distribution of the beamformed intensity. The deconvolution algorithm is further simplified with an approximate likelihood model (AM-DCV) that can reduce the computational complexity for each iteration. We employ a direct deconvolution method based on the Fourier transform to enhance the initial solution, thereby reducing the number of iterations required for convergence. The M-DCV and AM-DCV algorithms are validated using synthetic and experimental data, demonstrating a maximum improvement of 73% in angular resolution and a sidelobe suppression of 15 dB. Experimental examples demonstrate that the imaging performance of the deconvolution algorithm based on a linear small-aperture array consisting of 16 array elements is comparable to that obtained through conventional beamforming using a linear large-aperture array consisting of 96 array elements. The proposed algorithm is applicable for Ocean Acoustic Waveguide Remote Sensing (OAWRS) and other sensing applications using linear arrays. [ABSTRACT FROM AUTHOR]

In mechanical equipment, rolling bearing components are constantly exposed to intricate and diverse environmental conditions, rendering them vulnerable to wear, performance degradation, and potential malfunctions. To precisely extract and discern rolling bearing vibration signals amidst intricate noise interference, this paper introduces a fault feature extraction and diagnosis methodology that seamlessly integrates an improved Fourier decomposition method (FDM), singular value decomposition (SVD), and maximum second-order cyclostationary blind convolution (CYCBD). Initially, the FDM is employed to meticulously decompose the bearing fault signals into numerous signal components. Subsequently, a comprehensive weighted screening criterion is formulated, aiming to strike a balance between multiple indicators, thereby enabling the selective screening and reconstruction of pertinent signal components. Furthermore, SVD and CYCBD techniques are introduced to carry out intricate processing and envelope demodulation analysis of the reconstructed signals. Through rigorous simulation experiments and practical rolling bearing fault diagnosis tests, the method's noteworthy effectiveness in suppressing noise interference, enhancing fault feature information, and efficiently extracting fault features is unequivocally demonstrated. Furthermore, compared to traditional time–frequency analysis methods such as EMD, EEMD, ITD, and VMD, as well as traditional deconvolution methods like MED, OMEDA, and MCKD, this method exhibits significant advantages, providing an effective solution for diagnosing rolling bearing faults in environments with strong background noise. [ABSTRACT FROM AUTHOR]

It is known that image priors are essential to blind deconvolution. Reweighted graph total variation (RGTV), as a new prior to substitute the most classical total variation (TV), has been shown superior to TV and several other cutting-edge models both theoretically and empirically. This paper steps forward, firstly providing a simpler geometric perspective to RGTV in the framework of variational partial differential equations (PDEs), rather than the previous graph spectral interpretation made in the graph frequency domain. Surprisingly, a slight shift of perspective as such finally leads to a huge blind deblurring performance boosting in both accuracy and efficiency as compared to the previously derived numerical approach, which approximates RGTV as the graph L1-Laplacian regularizer. Utilizing the simplified RGTV as reformulated in this paper, another valuable contribution is an exploration of its potentials for blind facial image restoration by combining unsupervised deep facial models. Experimental results of blind face deblurring and blind face hallucination both demonstrate necessity and rationale of a joint model-based and learning-based approach to blind face restoration. [ABSTRACT FROM AUTHOR]

High‐precision P‐wave and S‐wave velocity models are very important for seabed exploration. Elastic full‐waveform inversion is an effective way to obtain the velocity models. Full‐waveform inversion is strongly dependent on source wavelet, and inaccurate wavelet estimation will severely affect the inversion results. Furthermore, elastic full‐waveform inversion is a highly non‐linear problem and has larger calculation and memory cost. Based on the deconvolution method, we develop a multi‐scale source‐independent elastic full‐waveform inversion method in a hybrid domain to alleviate the non‐linearity, to improve computation efficiency and decrease memory cost and to reduce the influence of source wavelet. We reconstruct the deconvoluted objective function and further derive the adjoint source and gradient formulas for elastic full‐waveform inversion with the adjoint‐state method. We can obtain good inversion results by using this objective function, adjoint source and gradient even if the source wavelet is unknown. In order to illustrate the influence of different reference traces on the objective function, we provide the theoretical formula of the objective function changing with the variation of reference traces. Experiments show that the deconvolution objective function cannot completely eliminate the influence of inaccurate source wavelet on the inversion, and the inversion effect depends on the selection of reference trace. Different inversion results of the Marmousi2 model indicate that the minimum offset trace is the best reference trace. Comparison of the inverted Marmousi2 model by the proposed method and the conventional elastic full‐waveform inversion method using correct wavelet shows that the two inversion results are very close, which proves the effectiveness of the proposed method and indicates a potential application of the method in seabed exploration. [ABSTRACT FROM AUTHOR]

Blind deconvolution (BD) has proven to be an effective approach to detecting repetitive transients caused by bearing faults. However, BD suffers from instability issues including excessive sensitivity of kurtosis-guided BD methods to the single impulse and high computational time cost of the eigenvector algorithm-aided BD methods. To address these critical issues, this paper proposed a novel BD method maximizing negative entropy (NE), shortened as maximum negative entropy deconvolution (MNED). MNED utilizes NE instead of kurtosis as the optimization metric and optimizes the filter coefficients through the objective function method. The effectiveness of MNED in enhancing repetitive transients is illustrated through a simulation case and two experimental cases. A quantitative comparison with three existing BD methods demonstrates the advantages of MNED in fault detection and computational efficiency. In addition, the performance of the four methods under different filter lengths and external shocks is compared. MNED exhibits lower sensitivity to random impulse noise than the kurtosis-guided BD methods and higher computational efficiency than the BD methods based on the eigenvalue algorithm. The simulation and experimental results demonstrate that MNED is a robust and cost-effective method for bearing fault diagnosis and condition monitoring. [ABSTRACT FROM AUTHOR]

This paper considers a partially linear regression model relating a right-censored response variable to predictors and an extra covariate with measured error. The main problem here is that censorship and measurement error problems need to be solved to estimate the model correctly. In this sense, we propose three modified semiparametric estimators obtained from local polynomial regression, kernel smoothing, and B-spline smoothing methods based on kernel deconvolution approach and synthetic data transformation. Here, kernel deconvolution technique is used to solve the measurement error problem in the model and synthetic data transformation is considered to add the effect of censorship to the estimation procedure, which is a very common method in the literature. The performances of the introduced estimators are compared in the detailed Monte-Carlo simulation study. In addition, Carotid endarterectomy data is used as real-world data example and results are presented. According to the results, it is seen that the deconvoluted local polynomial method gives more qualified estimates than other two methods. [ABSTRACT FROM AUTHOR]

We have developed a novel deconvolution‐based reverse time migration method to image lithospheric structures using teleseismic data recorded by dense seismic arrays. Unlike traditional approaches that rely on the retrieval of Green's functions (or receiver functions), the new method directly utilizes the recorded three‐component (3‐C) seismic waveforms to reconstruct subsurface wavefields, which has the advantage of avoiding the estimation and removal of source time function. Importantly, it enables the asymptotic estimation of P‐to‐S transmission conversion coefficients at the elastic discontinuities and enhances resolving power for the fine‐scale heterogeneities. Taking these improvements, we have obtained a full three‐dimensional (3‐D) high‐resolution image of the subduction zone beneath southwest Japan. This image provides a comprehensive configuration of the severely deformed subducting plate beneath the Kii Channel and Kinki Peninsula. Plain Language Summary: Wave equations based seismic imaging method theoretically possesses the most effective capacity for characterizing crustal and upper mantle strong laterally heterogeneous structures. However, its advantages have not been well manifested in the imaging of lithospheric structures, primarily due to the uncertainties introduced by the laborious data preprocessing to remove the complex source‐side effects associated with each earthquake event. To address these uncertainties, we propose a novel method to automatically eliminate source side effects by introducing a deconvolution imaging condition. This enables the direct use of three‐component seismic records only requiring some fundamental preprocessing, such as retrending, remeaning, tapering, and band‐pass filtering, to image the Earth's interior structures. Accordingly, the first attempt of full three‐dimensional elastic imaging beneath southwest Japan is intriguing, and unveils more detailed structures of the subduction zones compared to previous studies. Key Points: Deconvolution imaging condition is proposed for elastic reverse‐time migration of teleseismic waveforms with minimal data preconditioningComplex influence of source time function and long‐distance propagation of the incident wavefield is effectively handledThree‐dimensional elastic reverse time migration image beneath southwest Japan reveals more detailed structures of the Philipine Sea plate [ABSTRACT FROM AUTHOR]

Using computational tools, bulk transcriptomics can be deconvoluted to estimate the abundance of constituent cell types. However, existing deconvolution methods are conditioned on the assumption that the whole study population is served by a single reference panel, ignoring person-to-person heterogeneity. Here, we present imply, a novel algorithm to deconvolute cell type proportions using personalized reference panels. Simulation studies demonstrate reduced bias compared with existing methods. Real data analyses on longitudinal consortia show disparities in cell type proportions are associated with several disease phenotypes in Type 1 diabetes and Parkinson's disease. imply is available through the R/Bioconductor package ISLET at https://bioconductor.org/packages/ISLET/. [ABSTRACT FROM AUTHOR]

Understanding gene expression in different cell types within their spatial context is a key goal in genomics research. SPADE (SPAtial DEconvolution), our proposed method, addresses this by integrating spatial patterns into the analysis of cell type composition. This approach uses a combination of single-cell RNA sequencing, spatial transcriptomics, and histological data to accurately estimate the proportions of cell types in various locations. Our analyses of synthetic data have demonstrated SPADE's capability to discern cell type-specific spatial patterns effectively. When applied to real-life datasets, SPADE provides insights into cellular dynamics and the composition of tumor tissues. This enhances our comprehension of complex biological systems and aids in exploring cellular diversity. SPADE represents a significant advancement in deciphering spatial gene expression patterns, offering a powerful tool for the detailed investigation of cell types in spatial transcriptomics. SPADE integrates single-cell RNA sequencing, spatial transcriptomics, and histological data to estimate cell type composition, enhancing understanding of cellular dynamics and tumor tissue diversity. [ABSTRACT FROM AUTHOR]

Impulsive blind deconvolution (IBD) is a popular method to recover impulsive sources for bearing fault diagnosis. Its underpinnings are in the design of objective functions based on prior knowledge of impulsive sources and a transfer function to describe transmission path influences. However, popular objective functions cannot retain waveform impulsiveness and periodicity cyclostationarity simultaneously, and the single convolution operation of IBD methods is insufficient to describe transmission paths composed of multiple linear and nonlinear units. Inspired by the MaxPooling period modulation intensity (MPMI) and convolutional sparse learning (CSL), an adaptive multi-D-norm-driven sparse unfolding deconvolution network (AMD-SUDN) is proposed in this paper. The core strategy is that one target vector with simultaneous impulsiveness and cyclostationarity is constructed automatically through the MPMI; then, this vector is substituted into the multi D-norm to design objective functions. Moreover, an iterative soft threshold algorithm (ISTA) for the CSL model is derived, and its iterative steps are unfolded into one deconvolution network. The algorithm's performance and the hyperparameter configuration are investigated by a set of numerical simulations. Finally, the proposed AMD-SUDN is applied to detect the impulsive features of bearing faults. All comparative results verify that the proposed AMD-SUDN achieves a better deconvolution accuracy than state-of-the-art IBD methods. [ABSTRACT FROM AUTHOR]

Background: Tomosynthesis systems are three‐dimensional (3‐D) medical imaging devices that operate over limited acquisition angles using low radiation dosages. To measure the spatial resolution performance of a tomosynthesis system, the modulation transfer function (MTF) is widely used as a quantitative evaluation metric. Purpose: We previously introduced a method to estimate the full 3‐D MTF of a cone‐beam computed tomography system using two‐dimensional (2‐D) Richardson‐Lucy (RL) deconvolution with Tikhonov–Miller regularization. However, this method can not be applied directly to estimate the 3‐D MTF of a tomosynthesis system, since the unique artifacts (i.e., shadow artifacts, spreading tails, directional blurring, and high‐level noise) of the system produce several errors that lower the estimation performance. Varying positions of the negative pixels due to shadow artifacts and spreading tails cause inconsistent deconvolution performances at each of the directional projections, and the severe noise in the reconstructed images cause noise amplification during estimation. This work proposes several modifications to the previous method to resolve the inconsistent performance and noise amplification errors to increase the full 3‐D MTF estimation accuracy. Methods: Three modifications were introduced to the 2‐D RL deconvolution to prevent estimation errors and improve MTF estimation performance: non‐negativity relaxation function, cost function to terminate the iterative process of RL deconvolution, and regularization strength for noise control. To validate the effectiveness of the proposed modifications, we reconstructed sphere phantoms from simulation and experimental tomosynthesis studies in the iso‐center and offset‐center positions as well as estimated the full 3‐D MTFs using the previous and proposed methods. We compared the 3‐D render images, central plane images, and center profiles of the estimated 3‐D MTFs and calculated the full widths at half and tenth maximum for quantitative evaluation. Results: The previous method cannot estimate the full 3‐D MTF of a tomosynthesis system; its inaccurate negative pixel relaxation produces circular‐shaped errors, and the mean squared error based simple cost function for termination causes inconsistent estimation at each directional projection to diminish the clear edges of the low‐frequency drop and missing sample regions. Noise amplification from lack of noise regularization is also seen in the previous method results. Compared to the previous method, the proposed method shows superior estimation performance at reducing errors in both the simulation and experimental studies regardless of object position. The proposed method preserves the low‐frequency drop, missing sample regions from the limited acquisition angles, and missing cone region from the offset‐center position; the estimated MTFs also show FWHM and FWTM values close to those of the ideal MTFs than with the previous method. Conclusions: This work presents a method to estimate the full 3‐D MTF of a tomosynthesis system. The proposed modifications prevent circular‐shaped errors and noise amplification due to the geometry for limited acquisition angles and high noise levels. Compared to our previous method, the proposed scheme show better performance for estimating the 3‐D MTF of the tomosynthesis system. [ABSTRACT FROM AUTHOR]

Mineral exploration projects can make considerable use of a variety of geophysical techniques and datasets, including magnetic and gravity data. The interpretation of large quantities of data can be very time consuming, so semi-automatic interpretation techniques are often used to provide initial estimates of the parameters (primarily the location and depth) of the sources of anomalies. Euler deconvolution is a commonly used interpretation method for potential fields which has a number of advantages over many other techniques, such as working in the presence of remanent magnetisation, and not being restricted to a particular model such as a contact. A second-order version of Euler's equation is introduced here, which is much less affected by trends in the data than the standard method and additionally produces depth parabolas, which simplify the interpretation of results. The method was applied to aeromagnetic data from a mineral exploration project in Southern Africa and provided plausible results. [ABSTRACT FROM AUTHOR]

We develop a new deconvolution method to recover the precise Crab Nebula image taken by the Hitomi HXT, suppressing the artifact due to the bright Crab pulsar. We extend the Richardson–Lucy method, introducing two components corresponding to the nebula and pulsar with regularization for smoothness and flux, respectively, and performing simultaneous deconvolution of multi-pulse-phase images. The structures, including the torus and jets, seen in the deconvolved nebula image at the lowest energy band of 3.6–15 keV appear consistent with those identified in the high-resolution Chandra X-ray image. Above 15 keV, we confirm NuSTAR's findings that the nebula size decreases in higher energy bands. We find that the north-east side of the nebula is fainter in higher energy bands. Our deconvolution method is applicable for any telescope images of faint diffuse objects containing a bright point source. [ABSTRACT FROM AUTHOR]

In the process of seismic wave propagation, high-frequency energy is absorbed and attenuated by the stratum, and the dominant frequency and resolution decrease. To recover the energy of the high-frequency attenuation of seismic waves, a high-resolution processing method of time–frequency domain combined deconvolution (TFCD) is proposed. This method is different from the traditional time–frequency domain deconvolution because it considers the theory that the wavelet amplitude spectrum is smooth and has a low frequency. Wavelet separation is first conducted in the secondary spectral domain of seismic records and then smoothed in the log-domain to extract the time–frequency domain wavelet, which improves the accuracy of time–frequency domain deconvolution. This method comprehensively considers the wavelet shape and frequency characteristics, and can effectively improve seismic data resolution. [ABSTRACT FROM AUTHOR]

This paper presents a new accelerated proximal Markov chain Monte Carlo methodology to perform Bayesian inference in imaging inverse problems with an underlying convex geometry. The proposed strategy takes the form of a stochastic relaxed proximal-point iteration that admits two complementary interpretations. For models that are smooth or regularized by Moreau-Yosida smoothing, the algorithm is equivalent to an implicit midpoint discretization of an overdamped Langevin diffusion targeting the posterior distribution of interest. This discretization is asymptotically unbiased for Gaussian targets and shown to converge in an accelerated manner for any target that is κ-strongly log-concave (i.e., requiring in the order of √κ iterations to converge, similar to accelerated optimization schemes), comparing favorably to Pereyra, Vargas Mieles, and Zygalakis [SIAM J. Imaging Sci., 13 (2020), pp. 905-935], which is only provably accelerated for Gaussian targets and has bias. For models that are not smooth, the algorithm is equivalent to a Leimkuhler-Matthews discretization of a Langevin diffusion targeting a Moreau-Yosida approximation of the posterior distribution of interest and hence achieves a significantly lower bias than conventional unadjusted Langevin strategies based on the Euler-Maruyama discretization. For targets that are κ-strongly log-concave, the provided nonasymptotic convergence analysis also identifies the optimal time step, which maximizes the convergence speed. The proposed methodology is demonstrated through a range of experiments related to image deconvolution with Gaussian and Poisson noise with assumption-driven and data-driven convex priors. Source codes for the numerical experiments of this paper are available from https://github.com/MI2G/accelerated-langevin-imla. [ABSTRACT FROM AUTHOR]

This paper presents a novel stochastic optimization methodology to perform empirical Bayesian inference in semi-blind image deconvolution problems. Given a blurred image and a parametric class of possible operators, the proposed optimization approach automatically calibrates the parameters of the blur model by maximum marginal likelihood estimation, followed by (non-blind) image deconvolution by maximum a posteriori estimation conditionally to the estimated model parameters. In addition to the blur model, the proposed approach also automatically calibrates the noise level as well as any regularization parameters. The marginal likelihood of the blur, noise, and regularization parameters is generally computationally intractable, as it requires calculating several integrals over the entire solution space. Our approach addresses this difficulty by using a stochastic approximation proximal gradient optimization scheme, which iteratively solves such integrals by using a Moreau- Yosida regularized unadjusted Langevin Markov chain Monte Carlo algorithm. This optimization strategy can be easily and efficiently applied to any model that is log-concave and by using the same gradient and proximal operators that are required to compute the maximum a posteriori solution by convex optimization. We provide convergence guarantees for the proposed optimization scheme under realistic and easily verifiable conditions and subsequently demonstrate the effectiveness of the approach with a series of deconvolution experiments and comparisons with alternative strategies from the state of the art [ABSTRACT FROM AUTHOR]

Frequency-dependent equivalent linear (FD-EQL) site response analysis methods, developed as potential substitutes for the EQL procedure to better simulate the nonlinear soil response, have been reported to overpredict the high-frequency wave propagation. Modified procedures proposed to overcome this limitation have demonstrated to improve the fits with the nonlinear analysis results. The method has not yet been applied to perform a deconvolution analysis, where a conventional EQL analysis often fails to converge or provide reliable estimate. The conventional EQL procedure and one of the modified FD-EQL method, which uses an empirical factor f to interpolate the strain spectrum between the EQL and FD-EQL outputs, are used to perform a series of deconvolution analyses using an idealized 1000 m profile and twelve Kik-net downhole arrays. The residuals of recorded and deconvoluted motions are shown to increase with strain for the EQL method even when using the recommended frequency cut-off. For the FD-EQL method, the range of f recommended for convolution analyses is shown to provide unrealistic responses in performing deconvolution analyses. A new range that produces unbiased residuals for all strain amplitudes is proposed. Comparisons highlight that the modified FD-EQL yields reliable predictions of the within motion for all profiles and motion intensities, automatically suppressing the amplification of high-frequency noise typically accompanied in a deconvolution analysis. [ABSTRACT FROM AUTHOR]

Background: Medical image segmentation is one of the most key steps in computer‐aided clinical diagnosis, geometric characterization, measurement, image registration, and so forth. Convolutional neural networks especially UNet and its variants have been successfully used in many medical image segmentation tasks. However, the results are limited by the deficiency in extracting high resolution edge information because of the design of the skip connections in UNet and the need for large available datasets. Purpose: In this paper, we proposed an edge‐attending polar UNet (EPolar‐UNet), which was trained on the polar coordinate system instead of classic Cartesian coordinate system with an edge‐attending construction in skip connection path. Methods: EPolar‐UNet extracted the location information from an eight‐stacked hourglass network as the pole for polar transformation and extracted the boundary cues from an edge‐attending UNet, which consisted of a deconvolution layer and a subtraction operation. Results: We evaluated the performance of EPolar‐UNet across three imaging modalities for different segmentation tasks: CVC‐ClinicDB dataset for polyp, ISIC‐2018 dataset for skin lesion, and our private ultrasound dataset for liver tumor segmentation. Our proposed model outperformed state‐of‐the‐art models on all three datasets and needed only 30%–60% of training data compared with the benchmark UNet model to achieve similar performances for medical image segmentation tasks. Conclusions: We proposed an end‐to‐end EPolar‐UNet for automatic medical image segmentation and showed good performance on small datasets, which was critical in the field of medical image segmentation. [ABSTRACT FROM AUTHOR]

Thermal response test interpretation methods usually rely on the assumptions of constant operating conditions in time. However, through desired or undesired processes, these conditions often vary in time. Since interpretation is usually done with stationary methods, no current algorithm allows to account for non-stationarity in thermal response test, as encountered with varying flow rate. The goal of this article is to apply a multi-deconvolution algorithm to retrieve a set of short-term transfer functions during a thermal response test with changing operating conditions. The deconvolution algorithm uses an optimization-based technique as the inverse model, while considering non-stationarity in the forward model through a recent non-stationary convolution algorithm. By optimizing a set of nodes on each estimated short-term transfer function, precise reconstruction of the experimental temperatures is possible. Results show that temperature reconstruction is as precise as an error of 0.06 °C on numerical cases and 0.07 °C on field cases. The usable transfer function duration and an analysis of the objective function's optimum are also demonstrated. With the proposed algorithm, only the dataset of a thermal response test is needed to obtain short-term transfer functions when operating conditions are changing. [ABSTRACT FROM AUTHOR]

Deconvolution methods have been widely used in machinery fault diagnosis. However, their application would be confined due to the heavy noise and complex interference since the fault feature in the measured signal becomes rather weak. Time synchronous averaging (TSA) can enhance the periodic components and suppress the others by the comb filter function. And in the iteration process of the deconvolution methods, the filtered signal after each iteration can be further processed using TSA, and the time delay with maximum Gini index value is refined as the iterative period for the next iteration. Benefitting from these advantages, a period-refined maximum second-order cyclostationarity blind deconvolution (PRCYCBD) using TSA is proposed for the weak fault detection of rolling element bearings (REBs) in this paper. Firstly, without any prior knowledge, the proposed method which can estimate the period more accurately is more suitable for the weak fault detection of REBs, especially incipient fault. Secondly, TSA is firstly applied to estimate the iterative period rather than just depending on the Signal Noise Ratio (SNR) of the filtered signal in the iterative process. Furthermore, the new improvement frame can be expanded to other deconvolution methods using iterative algorithms, especially under heavy noise. Finally, a simulation with a slight bearing fault as well as two real experimental data including the vibration signal with the wind turbine bearing fault and the acoustical signal with the locomotive wheel bearing fault is used to verify the superiority of the proposed PRCYCBD compared with the traditional minimum entropy deconvolution and the traditional autocorrelation-improved cyclostationarity blind deconvolution. [ABSTRACT FROM AUTHOR]

We propose a new approach to solving bilevel optimization problems, intermediate between solving full-system optimality conditions with a Newton-type approach, and treating the inner problem as an implicit function. The overall idea is to solve the full-system optimality conditions, but to precondition them to alternate between taking steps of simple conventional methods for the inner problem, the adjoint equation, and the outer problem. While the inner objective has to be smooth, the outer objective may be nonsmooth subject to a prox-contractivity condition. We prove linear convergence of the approach for combinations of gradient descent and forward-backward splitting with exact and inexact solution of the adjoint equation. We demonstrate good performance on learning the regularization parameter for anisotropic total variation image denoising, and the convolution kernel for image deconvolution. [ABSTRACT FROM AUTHOR]