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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]

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]

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]

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]

In the multidimensional setting, we consider the nonparametric regression estimation with errors-in-variables. Both ordinary smooth noise and super smooth one are assumed for errors in the covariates. An anisotropic kernel estimator is provided based on a deconvolution technique. We study the pointwise estimation and obtain the optimal rates of convergence under the anisotropic Hölder condition. [ABSTRACT FROM AUTHOR]

This paper evaluates the effects of Soil-Structure Interaction (SSI) on the seismic response of multi-story concrete frames subjected to earthquake ground motions. To calculate the structural response, an iterative Wave-Propagation (WP) based method has been used. The exact solution of SSI problems, in addition to high computational costs, due to general complexity of finite element analysis, require an advanced computer system. According to the method proposed herein, buildings were modelled as an extension of the layered soil media by considering each story as a layer in the WP path. The motion in each layer could be determined from the motion in any other layer. This permitted to use an operation called deconvolution, which could be considered to investigate the effect of substructure soil layers on the structural response. One of the capabilities of WP method is to facilitate the computation of bedrock motion from a known free surface motion and consequently determination of correct foundation input motion. While most of the current methods assume constant values for basic parameters such as; stiffness and damping, in the present method in order to investigate the nonlinear behaviour, stiffness and damping are proportional to the displacement level of soil layers or structural floors. The computational speed and accuracy of the proposed method are also verified by a benchmark frame analysis. Also, based on the Park-Ang Damage Index, this paper evaluated the measures of damage (the relationship between earthquake characteristics (PGA) and damage level) which govern structural degradation and/or collapse obtained from different well-known destructive earthquakes. [ABSTRACT FROM AUTHOR]

We investigate the effectiveness of convex relaxation and nonconvex optimization in solving bilinear systems of equations under two different designs (i.e., a sort of random Fourier design and Gaussian design). Despite the wide applicability, the theoretical understanding about these two paradigms remains largely inadequate in the presence of random noise. The current article makes two contributions by demonstrating that (i) a two-stage nonconvex algorithm attains minimax-optimal accuracy within a logarithmic number of iterations, and (ii) convex relaxation also achieves minimax-optimal statistical accuracy vis-à-vis random noise. Both results significantly improve upon the state-of-the-art theoretical guarantees. for this article are available online. [ABSTRACT FROM AUTHOR]

Reducing multiple contaminations in reflection seismic data remains one of the primary challenges in marine seismic data processing. Besides geological settings, its effectiveness is also dependent on the multiple removal methods. In this study, we undertook two legacy 2D multi-channel seismic data crossing the accretionary wedge off SW Taiwan to test the efficiency of various multiple-attenuation scenarios. The tectonic domain has resulted from the incipient arc-continent collision between the northern rifted margin of the South China Sea and the Luzon volcanic arc. The wedge extends from shallow water to deep water bathymetries, hence promoting both short-period and long-period multiples within the seismic records. A cascade of de-multiple methods was tested to attenuate multiple energy under various seafloor bathymetry and tectonic areas. The first step relies on the periodicity nature of multiples. Spatial dependent predictive deconvolution in the x-t domain was performed to attenuate reverberations and improve temporal resolution in the time domain. Wave-equation multiple attenuation (WEMA) was applied to suppress the water layer multiples based on a combination of numerical wave extrapolation in the shot domain through water layer and water bottom reflectivity. Surface-related multiple elimination (SRME) aimed to attenuate the residual water bottom multiple and peg-leg multiple by assuming surface-related multiples can be kinematically predicted via convolution of pre-stack seismic traces at possible surface multiple reflection locations. The second step exploits the spatial move-out difference behavior between primaries and multiples. Parabolic Radon transforms far-offset multiples by subtracting noise energy in the τ-p domain, whereas the frequency-wave number (F-K) filter aimed to eliminate any residual multiples energy in the F-K domain. Predictive deconvolution improved seismic resolution and suppressed sea-bottom reverberation energy in the continental and lower wedge slopes, but not in the upper wedge slope. WEMA, Radon filter, and F-K filter reduced multiples energy both at the continental slope and wedge slope; whereas SRME made minimal impact on both areas. Since the reflection seismic datasets stretch diverse tectonic environments and water depth, there was no single multiple attenuation method capable to suppress multiples in all tectonic environments and bathymetry. [ABSTRACT FROM AUTHOR]

Blind image deconvolution recovers a deblurred image and the blur kernel from a blurred image. From a mathematical point of view, this is a strongly ill-posed problem and several works have been proposed to address it. One successful approach proposed by Chan and Wong consists in using the total variation (TV) as a regularization for both the image and the kernel. These authors also introduced an Alternating Minimization (AM) algorithm in order to compute a physical solution. Unfortunately, Chan's approach suffers in particular from the ringing and staircasing effects produced by the TV regularization. To address these problems, we propose a new model based on Bilateral Total Variation (BTV) regularization of the image keeping the same regularization for the kernel. We prove the existence of a minimizer of a proposed variational problem in a suitable space using a relaxation process. We also propose an AM algorithm based on our model. The efficiency and robustness of our model are illustrated and compared with the TV method through numerical simulations. [ABSTRACT FROM AUTHOR]

Estimating the marginal and joint densities of the long-term average intakes of different dietary components is an important problem in nutritional epidemiology. Since these variables cannot be directly measured, data are usually collected in the form of 24-hour recalls of the intakes. The problem of estimating the density of the latent long-term average intakes from their observed but error contaminated recalls then becomes a problem of multivariate deconvolution of densities. The underlying densities could potentially vary with the subjects' demographic characteristics such as sex, ethnicity, age, etc. The problem of density deconvolution in the presence of associated precisely measured covariates has, however, never been considered before, not even in the univariate setting. We present a flexible Bayesian semiparametric approach to covariate informed multivariate deconvolution. Building on recent advances on copula deconvolution and conditional tensor factorization techniques, our proposed method not only allows the joint and the marginal densities to vary flexibly with the associated predictors but also allows automatic selection of the most influential predictors. Importantly, the method also allows the density of interest and the density of the measurement errors to vary with potentially different sets of predictors. We design Markov chain Monte Carlo algorithms that enable efficient posterior inference, appropriately accommodating uncertainty in all aspects of our analysis. The empirical efficacy of the proposed method is illustrated through simulation experiments. Its practical utility is demonstrated in the afore-described nutritional epidemiology applications in estimating covariate adjusted long term intakes of different dietary components. An important by-product of the approach is a solution to covariate informed ordinary multivariate density estimation. include substantive additional details and R codes are also available online. [ABSTRACT FROM AUTHOR]

This paper is devoted to a nonparametric estimation of the probability θ : = ℙ (X < Y) , where X, Y are continuous univariate random variables of interest and observed with additional random errors. We focus on the case where the distributions of the random errors are unknown but symmetric around zero and can be estimated from some additional samples. Using deconvolution techniques, we propose an estimator of θ which depends on a regularization parameter. We then establish upper and lower bounds on convergence rate of the estimator under mean squared error when error densities are assumed to be supersmooth. [ABSTRACT FROM AUTHOR]

A method that combines Lucy-Richardson deconvolution algorithm (LRA) with a multiview projection setup to improve imaging reconstruction of objects embedded in scattering media is presented. In the first step, the medium was illuminated with a laser beam and single-shot multiple images of the object were obtained from different viewpoints. Next, the above procedure was performed under the same conditions but only the medium, without the object, was illuminated by a light point source to obtain the system PSF. Third, each sub-image of the object was digitally cropped, extracted from the array, and deconvolved with the average PSF image following the LRA. Finally, all the sub-deconvolved images were shifted to a common point and superimposed to reveal the shape of the hidden object. Various setup conditions including medium turbidity, thickness, target shape, and illumination state were tested and compared. Results indicate an effective performance of the proposed method. [ABSTRACT FROM AUTHOR]

Generative adversarial networks (GANs) have effectively promoted the development of hyperspectral image classification technology in generating samples. Many GAN-based models for hyperspectral image classification use deconvolution to generate fake samples, which will cause chequerboard artefacts and affect classification performance. Furthermore, the training of GANs still faces the problem of mode collapse. Aiming at the above problems, we proposed a dual hybrid convolutional generative adversarial network (DHCGAN) for hyperspectral image classification. Firstly, the combination of nearest neighbour upsampling and sub-pixel convolution is employed in the generator, which avoids the overlap of convolution domain and effectively suppresses the chequerboard artefacts caused by deconvolution. Secondly, the traditional convolution and dilated convolution are fused in the discriminator, which expands the receptive field without increasing parameters and achieves more effective feature extraction. In addition, some adaptive drop blocks are embedded into the generator and discriminator to effectively alleviate the problem of mode collapse. Experiments were performed on four hyperspectral datasets (including three classical datasets – Indian Pines, University of Pavia and Houston, a new dataset – WHU-Hi-HanChuan). Experimental results show that the proposed method can provide a certain performance improvement over some competing methods, such as the accuracy has been increased by more than 1% on the three classical datasets, and even got over 3% improvement on WHU_Hi_HanChaun dataset. [ABSTRACT FROM AUTHOR]

Anisotropic functional deconvolution model is investigated in the bivariate case when the design points ti, i = 1 , 2 , ⋯ , N , and xl, l = 1 , 2 , ⋯ , M , are irregular and follow known densities h1, h2, respectively. In particular, we focus on the case when the densities h1 and h2 have singularities, but 1 / h 1 and 1 / h 2 are still integrable on [0, 1]. We construct an adaptive wavelet estimator that attains asymptotically near-optimal convergence rates in a wide range of Besov balls. The convergence rates are completely new and depend on a balance between the smoothness and the spatial homogeneity of the unknown function f, the degree of ill-posed-ness of the convolution operator and the degrees of spatial irregularity associated with h1 and h2. Nevertheless, the spatial irregularity affects convergence rates only when f is spatially inhomogeneous in either direction. [ABSTRACT FROM AUTHOR]

The venerable method of maximum likelihood has found numerous recent applications in nonparametric estimation of regression and shape constrained densities. For mixture models the nonparametric maximum likelihood estimator (NPMLE) of Kiefer and Wolfowitz plays a central role in recent developments of empirical Bayes methods. The NPMLE has also been proposed by Cosslett as an estimation method for single index linear models for binary response with random coefficients. However, computational difficulties have hindered its application. Combining recent developments in computational geometry and convex optimization, we develop a new approach to computation for such models that dramatically increases their computational tractability. Consistency of the method is established for an expanded profile likelihood formulation. The methods are evaluated in simulation experiments, compared to the deconvolution methods of Gautier and Kitamura and illustrated in an application to modal choice for journey-to-work data in the Washington DC area. for this article are available online. [ABSTRACT FROM AUTHOR]

We study the non-parametric estimation of an unknown survival function S with support on R + based on a sample with multiplicative measurement errors. The proposed fully data-driven procedure is based on the estimation of the Mellin transform of the survival function and a regularization of the inverse of the Mellin transform by a spectral cut-off. The upcoming bias-variance trade-off is handled by a data-driven choice of the cut-off parameter. In order to discuss the bias term, we consider the Mellin–Sobolev spaces which characterize the regularity of the unknown survival function S through the decay of its Mellin transform. For the analysis of the variance term, we consider the independent and identically distributed case and incorporate dependent observations in form of Bernoulli shift processes and β-mixing sequences. Additionally, we show minimax optimality over Mellin–Sobolev spaces of the spectral cut-off estimator. [ABSTRACT FROM AUTHOR]

The problem of estimating a function's derivative arises in many scientific settings, from medical imaging to astronomy. In this paper, we consider a hard thresholding wavelet approach to certain blind deconvolution problem based on the heteroscedastic data. Motivated by Delaigle & Meister's work, the adaptive wavelet estimators are proposed and their asymptotic properties are investigated. It is shown that the derivative estimators for the blind deconvolution model are spatially adaptive and attain the optimal rate of convergence up to a logarithmic factor over a range of Besov classes. Our theorems generalize the results of Cai and Navarro et al. in some sense. [ABSTRACT FROM AUTHOR]

Estimating the marginal and joint densities of the long-term average intakes of different dietary components is an important problem in nutritional epidemiology. Since these variables cannot be directly measured, data are usually collected in the form of 24-hr recalls of the intakes, which show marked patterns of conditional heteroscedasticity. Significantly compounding the challenges, the recalls for episodically consumed dietary components also include exact zeros. The problem of estimating the density of the latent long-time intakes from their observed measurement error contaminated proxies is then a problem of deconvolution of densities with zero-inflated data. We propose a Bayesian semiparametric solution to the problem, building on a novel hierarchical latent variable framework that translates the problem to one involving continuous surrogates only. Crucial to accommodating important aspects of the problem, we then design a copula based approach to model the involved joint distributions, adopting different modeling strategies for the marginals of the different dietary components. We design efficient Markov chain Monte Carlo algorithms for posterior inference and illustrate the efficacy of the proposed method through simulation experiments. Applied to our motivating nutritional epidemiology problems, compared to other approaches, our method provides more realistic estimates of the consumption patterns of episodically consumed dietary components. for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement. [ABSTRACT FROM AUTHOR]

Euler deconvolution is a widely used semiautomatic method for potential field data, but it produces sprays of solutions which complicate interpretation. It is demonstrated here that the accuracy of the solution locations can be improved if the method is applied iteratively. Euler deconvolution uses a window of datapoints to solve for the horizontal and vertical distances from the centre of the window to the potential field source. When applied iteratively the method uses the horizontal location of a solution to define the centre of a new window of data points. This new window of points is then used to generate an improved Euler solution, and the procedure is repeated. Solutions that are initially poorly located either migrate closer to potential field sources or diverge beyond the limits of the data, thus removing them from the result. The method is demonstrated on synthetic datasets and aeromagnetic data from South Africa. [ABSTRACT FROM AUTHOR]

This current paper considers a pointwise lower bound for generalized deconvolution density estimation under the local Hölder condition. Our result can be considered as extensions of the deconvolution density estimation and the classical density estimation with no errors. In addition, we do not assume that the noises are identically distributed in this paper. [ABSTRACT FROM AUTHOR]

Deconvolution is essential for high-resolution seismic data processing. Conventional deconvolution methods are either based on a stationary convolution model or under the assumption that Q factor and the source wavelet are known. However, in reality, seismic wavelet is usually unknown and time-varying during propagation due to attenuation. Thus, we propose a blind nonstationary deconvolution (BND) method which does not require advance Q factor and source wavelet as inputs and takes into account the lateral continuity of deconvolution results. Firstly, we develop an improved nonstationary convolution model consisting of the time-varying wavelet and reflectivity, which enables us to obtain reflectivity without attenuation estimation. To accommodate the changing frequency spectrum of seismic data, we present a time-varying wavelet estimation method using the frequency spectrum at every sample point and the generalised seismic wavelet function. By incorporating the extracted time-varying wavelet into the improved convolution model, we propose to formulate the objective function for reflectivity inversion as a joint low-rank and sparse inversion convex optimisation problem. It helps deconvolution results keep the sparsity in the vertical direction while maintaining the continuity in the horizontal direction. The performance of BND is evaluated through synthetic examples and a field data example. [ABSTRACT FROM AUTHOR]

In conventional vibroseis data processing, the recorded sweep is correlated with the recorded trace, assuming that the estimated groundforce is equal to the sweep, but it is demonstrated that due to the non-linearity associated with the vibrator system, the true groundforce and the recorded sweep are not the same. Further, while processing, it is assumed that the zero phase Klauder wavelet is convolved with the Earth's reflectivity, completely ignoring the fact that the far-field velocity is basically proportional to the time-derivative of the groundforce, hence on real data, it is not possible to achieve an ideal zero-phase wavelet. Additionally, the Earth's low-pass filtering generates a mixed-phase signal, which is not suitable for conventional deconvolution. We demonstrate that the recorded sweep contaminates the traces with harmonic noise and recommend a pre-determined sweep for cross-correlation. Further, to avoid minimum-phase violation issue, we endorse the frequency domain sweep deconvolution method (FDSD). Our results on synthetic as well as real seismic data, generated after FDSD, show significant improvement in resolution and noise suppression, as compared to the cross-correlated one. It was also shown that the predictive deconvolution combined with FDSD should be used to generate deconvolved seismic sections, and the spiking deconvolution should be avoided. [ABSTRACT FROM AUTHOR]

Advanced seismic detection technology utilising random roadway sources is advantageous method adapting to the development of dynamic intelligent technologies for the detection of hidden and disastrous geological structures. However, roadheaders generate complex signals, that are continuous and random with seismic wavelets that are wider and longer than conventional source wavelets, and these complex wavelets cannot be directly subjected to data processing. To address this problem, based on two basic techniques, namely, deconvolution and cross-correlation, a cross-correlation algorithm in the deconvolution domain is proposed to process continuous random roadheader signals, convert those signals into normal-impulse seismic data, and extract the arrivals of direct and reflected waves and other information. First, the feasibility of the algorithm is explained based on a derivation of theoretical formulas. Then, to verify the applicability of the algorithm to the processing of actual data, a random signal from a tamping source is processed; the continuous random signals are successfully converted into impulse signals, and the extracted in-phase direct waves are clear with good continuity. Moreover, the continuous random signal processing results are compared with an active source signal, and good consistency is found, verifying the effectiveness of the algorithm. Finally, an application analysis of the algorithm is carried out using an actual acquired roadheader source signal. After implementing the algorithm, the random roadheader signal is successfully converted into a normal-impulse seismic signal, and the direct wave arrivals are extracted. Based on the arrival times of the direct waves, the longitudinal wave velocity of the coal seam is calculated as 1918 m/s, which is consistent with the actual velocity. A comprehensive analysis of the test results confirms that the cross-correlation algorithm in the deconvolution domain is both feasible and effective and that the processed seismic signals can be used for subsequent processing and interpretation. [ABSTRACT FROM AUTHOR]

In the present paper, we consider the estimation of a periodic two-dimensional function f (· , ·) based on observations from its noisy convolution, and convolution kernel g (· , ·) unknown. We derive the minimax lower bounds for the mean squared error assuming that f belongs to certain Besov space and the kernel function g satisfies some smoothness properties. We construct an adaptive hard-thresholding wavelet estimator that is asymptotically near-optimal within a logarithmic factor in a wide range of Besov balls. The proposed estimation algorithm implements a truncation to estimate the wavelet coefficients, in addition to the conventional hard-thresholds. A limited simulations study confirms theoretical claims of the paper. [ABSTRACT FROM AUTHOR]

Immunotherapies have attracted lots of research interests recently. The need to understand the underlying mechanisms of immunotherapies and to develop precision immunotherapy regimens has spurred great interest in characterizing immune cell composition within the tumor microenvironment. Several methods have been developed to estimate immune cell composition using gene expression data from bulk tumor samples. However, these methods are not flexible enough to handle aberrant patterns of gene expression data, for example, inconsistent cell type-specific gene expression between purified reference samples and tumor samples. We propose a novel statistical method for expression deconvolution called immune cell deconvolution in tumor tissues (ICeD-T). ICeD-T automatically identifies aberrant genes whose expression are inconsistent with the deconvolution model and down-weights their contributions to cell type abundance estimates. We evaluated the performance of ICeD-T versus existing methods in simulation studies and several real data analyses. ICeD-T displayed comparable or superior performance to these competing methods. Applying these methods to assess the relationship between immunotherapy response and immune cell composition, ICeD-T is able to identify significant associations that are missed by its competitors. for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement. [ABSTRACT FROM AUTHOR]

The temperature dependence of the reduced activation energy w = ε/kBT of the conductivity σ has been utilised for determining the impurity conduction mechanism in doped semiconductors in many studies. Herein, the formula for deconvoluting w when plural conduction mechanisms appear is used to confirm the analysis of the data of the Hall-effect measurements on Al-doped n-ZnSe samples. The analysis is performed on the basis of an impurity-Hubbard-band model which includes ε2 conduction in the top Hubbard band as well as ε3 and Efros-Shklovskii (ES) variable-range hopping (VRH) conduction processes in the bottom Hubbard band. As the result of the analysis, transitions among the three hopping conduction mechanisms of ε2, ε3, and ES VRH are clearly shown in the temperature dependence of w as well as in that of the Hall mobility, which are hardly noticed in the temperature dependence of σ. In addition, the power-law exponent of the prefactor of ES VRH conductivity is determined through the fit to the temperature dependence of w to show that it decreases from ∼ 1.5 to ∼ 0 with increasing net donor concentration. [ABSTRACT FROM AUTHOR]

A new iterative algorithm is proposed to improve the detection of dim stellar objects that are in the neighbourhood of a bright object, using short-exposure images. This method separates data functions into the primary bright object function, the neighbourhood system function, and the background function. This approach uses the principles of the Expectation-Maximization algorithm with the Gerchberg-Saxton phase retrieval algorithm to overcome the image degradation caused by the photon counting noise from the charge-coupled devices and the turbulent atmospheric conditions. The performance of this new neighbourhood system algorithm is compared with that of the multiframe blind deconvolution algorithm, using laboratory data and computer-simulated data. This paper provides an improved technique to image closely spaced dim objects. [ABSTRACT FROM AUTHOR]

Distribution estimation for noisy data via density deconvolution is a notoriously difficult problem, especially for typical noise distributions like Gaussian. We develop a density deconvolution estimator based on quadratic programming (QP) that can achieve better estimation than kernel density deconvolution methods. The QP approach appears to have a more favorable regularization tradeoff between oversmoothing versus oscillation, especially at the tails of the distribution. An additional advantage is that it is straightforward to incorporate a number of common density constraints such as nonnegativity, integration-to-one, unimodality, tail convexity, tail monotonicity, and support constraints. We demonstrate that the QP approach has favorable estimation performance relative to existing methods. Its performance is superior when only the universally applicable nonnegativity and integration-to-one constraints are incorporated, and incorporating additional common constraints when applicable (e.g., nonnegative support, unimodality, tail monotonicity or convexity, etc.) can further substantially improve the estimation. for this article are available online and include R code, the R package QPdecon, a vignette for the QPdecon package, the sodium dataset that is used as an example, and appendices with a proof and additional figures. [ABSTRACT FROM AUTHOR]

The present study was aimed to optimize capsulated unfolding type gastroretentive bilayer film constituting immediate release (IR) layer of amlodipine besylate and sustained release (SR) layer of atorvastatin calcium. A three-factor, three-level Box–Behnken-design was used to optimize bilayer film with dual-release characteristics. The selected independent variables were HPMC-K3, Eudragit RSPO, and Carbopol 934P and the responses were floating duration, swelling index, and in vitro release from SR layer in 8 h. The films were also assessed for pharmacotechnical characteristics, release kinetics, DSC, FTIR, and SEM. The pharmacokinetics of the drugs from the optimized formulation was compared with the marketed formulation in rabbits. The capsulated accordion film unfolded and provided SR of atorvastatin for 8 h (96.76% ± 0.71) and IR of amlodipine within 25 min (98.07% ± 0.62) for the optimized formulation (F14). The swelling index and floating duration for the optimized formulation were 140.48 ± 0.57 and 8.53 ± 0.10 h, respectively. Results of pharmacokinetics showed that faster absorption of amlodipine and improved bioavailability (2.16-fold) of atorvastatin in blood was made available through bilayer film. In vitro–in vivo correlation was established using numerical deconvolution method. It can be concluded that the capsulated gastroretentive system provided site specific simultaneous SR of antihyperlidemic drug and IR of antihypertensive drug as single pill that has therapeutic potential to manage cardiovascular risk. [ABSTRACT FROM AUTHOR]

Recent research shows that deep learning-based methods can achieve promissing performance when applied to hyperspectral image (HSI) classification in remote sensing, some challenging issues still exist. For example, after a number of 2D convolutions, each feature map may only correspond to a unique dimension of the hyperspectral image. As a result, the relationship between different feature maps from multiple dimensional hyperspectral image can not be extracted well. Another issue is information in extracted feature maps may be erased by pooling operations. To address these problems, we propose a novel hybrid neural network (HNN) for hyperspectral image classification. The HNN uses a multi-branch architecture to extract hyperspectral image features in order to improve its prediction accuracy. Moreover, we build a deconvolution structure to recover the lost information in the pooling operation. In addition, to improve convergence and prevent overfitting, the HNN applies batch normalization (BN) and parametric rectified linear units (PReLU). In the experiments, two public benchmark HSIs are utilized to evaluate the performance of the proposed method. The experimental results demonstrate the superiority of HNN over several well-known methods. [ABSTRACT FROM AUTHOR]

In deconvolution in R d , d ≥ 1 , with mixing density p (∈ P) and kernel h, the mixture density f p (∈ F p) is estimated with MDE f p ˆ n , having upper L 1 -error rate, a n , in probability or in risk; p ˆ n ∈ P . In one application, P consists of L 1 -separable densities in R with differences changing sign at most J times and h (x − y) Totally Positive. When h is known and p is q ~ -smooth, vanishing outside a compact in R d , plug-in upper bounds are provided for the L 2 -error rate of p ˆ n and its [ s ] -th mixed partial derivative p ˆ n (s) , via ∥ f p ˆ n − f p ∥ 1 , with rates (log ⁡ a n − 1 ) − N 1 and a n N 2 , respectively, for h super-smooth and smooth; q ~ ∈ R + , [ s ] ≤ q ~ , d ≥ 1 , N 1 > 0 , N 2 > 0. For a n ∼ (log ⁡ n) ζ ⋅ n − δ , the former rate is optimal for any δ > 0 and the latter misses the optimal by the factor (log ⁡ n) ξ when δ =.5 ; ζ > 0 , ξ > 0. N 1 and N 2 appear in optimal rates and lower error and risk bounds in the deconvolution literature. [ABSTRACT FROM AUTHOR]

In this paper, we present a new method based on the reciprocal of the analytic signal amplitude and its derivatives, to directly estimate the structural indices and location parameters of 2D magnetic data. However, the method is sensitive to noise because third-order derivatives are used. To weaken the noise effect, we use a smooth compensation filtering method, based on a modification of upward continuation, to suppress high-frequency noise. The method successfully estimates the magnetic source parameters when tested on noise-free and noise-corrupted synthetic magnetic data. Moreover, when applied to synthetic data produced by multiple sources, the proposed method has higher precision and clustering of the solutions is tighter than for standard Euler deconvolution of the total magnetic intensity anomaly or of the analytic signal magnitude. The method is also applied to the measured magnetic data over the Urad Middle Banner in northeast China. [ABSTRACT FROM AUTHOR]

Impedance inversion performed on post-stack seismic data is one approach to reservoir prediction. Conventional post-stack seismic data inversion has two main stages. Stage one involves deconvolution to estimate reflectivities and stage two is estimation of the impedance section from these reflectivities. These two stages are ill-posed inverse problems due to the nature of seismic inversion. An alternative method has been proposed that combines the two stages to estimate seismic impedance directly. Because it is less sensitive to noise in the seismic data, the proposed method decreases the inherent ill-posedness of impedance inversion. To regularise this merged inverse problem, L0 gradient minimisation of impedance has been used. L0 gradient minimisation regularisation provides a blocky impedance solution that makes formation interfaces and geological edges more precise and keeps the inversion procedure robust even if random noise exists in the seismic data. A split-Bregman-like algorithm has been used to solve the L0 gradient minimisation problem. The results of numerical examples show that the proposed inversion method can generate more accurate impedance models compared with conventional methods. Finally, the proposed method is applied to real seismic data from east China to test its applicability in practice. The inversion results confirm that the proposed method is effective at inverting real seismic data. [ABSTRACT FROM AUTHOR]

In this work, a novel migration method is applied to Ground-Penetrating Radar (GPR) data to detect the internal flaws of ornamental stone blocks. To detect and classify fractures in accordance with their spatial orientation, a Shift-Invariant Probabilistic Latent Component Analysis (SI-PLCA) is proposed. GPR simulations are conducted using modeling software to test several types of fractures (with different positions, thicknesses, and lengths) in rock blocks and to train several patterns as inputs for the SI-PLCA method. An 800 MHz antenna is used to assess both simulated and real data. The accuracy rate of the proposed approach is evaluated and compared with that of classical migration methods for detection and is compared to a Template Matching approach for classification; promising results are obtained. In addition, GPR is applied to two blocks of a rock type known commercially as Crema Marfil. The 3D fracture maps obtained from the proposed approach are compared with the stone slabs from the cutting process. The results show that the proposed approach applied to GPR radargrams is an effective method for determining the internal structure of stone materials, particularly for detecting and classifying fractures. [ABSTRACT FROM AUTHOR]

We look into the minimax results for the anisotropic two-dimensional functional deconvolution model with the two-parameter fractional Gaussian noise. We derive the lower bounds for the -risk, , and taking advantage of the Riesz poly-potential, we apply a wavelet-vaguelette expansion to de-correlate the anisotropic fractional Gaussian noise. We construct an adaptive wavelet hard-thresholding estimator that attains asymptotically optimal or quasi-optimal convergence rates in a wide range of Besov balls. Such convergence rates depend on a delicate balance between the parameters of the Besov balls, the degree of ill-posedness of the convolution operator and the parameters of the fractional Gaussian noise under regular-smooth convolution, whereas the rates are not affected by long-memory under super-smooth convolution. A limited simulations study confirms the theoretical claims of the paper. The proposed approach is extended to the general r-dimensional case, with r>2, and the corresponding convergence rates do not suffer from the curse of dimensionality. [ABSTRACT FROM AUTHOR]

Semi-functional linear regression models are important in practice. In this paper, their estimation is discussed when function-valued and real-valued random variables are all measured with additive error. By means of functional principal component analysis and kernel smoothing techniques, the estimators of the slope function and the non parametric component are obtained. To account for errors in variables, deconvolution is involved in the construction of a new class of kernel estimators. The convergence rates of the estimators of the unknown slope function and non parametric component are established under suitable norm and conditions. Simulation studies are conducted to illustrate the finite sample performance of our method. [ABSTRACT FROM AUTHOR]

This work using piecewise polynomial fitting and third derivative methods accurately determined the initial modulus, yield point, specific work before and after the yield point of palm and ramie fibers. After the completion of the algorithm, no subjective factors were added in the calculation process. Palm fiber showed remarkable yield characteristics. The yield point, specific work of palm fibers both before and after the yield point decreased with the gage length, whereas the initial modulus and the ratio of BY to AY increased. Scanning electron microscopy(SEM) indicates that palm fiber can be considered as composite, whose de-bonding of single fibers and interlayer separation of cell wall contribute to the nonlinear de-formation. X-ray diffraction (XRD) peak deconvolution was confirmed as an effective method in disintegrating spectrogram. Results showed that the CI of ramie fibers (62.93%) was higher than that of palm fibers (34.13%), which considerably influenced the mechanical behavior of the fibers. The distinctive tensile properties of palm fiber may endow its potential application in industrial areas. [ABSTRACT FROM AUTHOR]

In this paper, we consider a statistical estimation problem known as atomic deconvolution. Introduced in reliability, this model has a direct application when considering biological data produced by flow cytometers. From a statistical point of view, we aim at inferring the percentage of cells expressing the selected molecule and the probability distribution function associated with its fluorescence emission. We propose here an adaptive estimation procedure based on a previous deconvolution procedure introduced by Es, Gugushvili, and Spreij [(2008), 'Deconvolution for an atomic distribution', Electronic Journal of Statistics, 2, 265–297] and Gugushvili, Es, and Spreij [(2011), 'Deconvolution for an atomic distribution: rates of convergence', Journal of Nonparametric Statistics, 23, 1003–1029]. For both estimating the mixing parameter and the mixing density automatically, we use the Lepskii method based on the optimal choice of a bandwidth using a bias-variance decomposition. We then derive some convergence rates that are shown to be minimax optimal (up to some log terms) in Sobolev classes. Finally, we apply our algorithm on the simulated and real biological data. [ABSTRACT FROM AUTHOR]

The observed data are usually contaminated by various errors in practical applications. This paper deals with the density deconvolution problems with super smooth errors under heteroscedastic situation. We provide a new wavelet estimator and investigate its upper bound of Lp risk over Besov ball. Then the lower bound is given which shows that the defined estimator attains the optimal convergence rate. It turns out that Theorem 3.1 extends some existing theorems of Pensky and Vidakovic, Fan and Koo, as well as Li and Liu in some sense. However, since the convergence is just logarithmic rate which is not satisfactory for us. Motivated by the works of Pensky and Vidakovic, Li and Liu, we study the wavelet estimator over super smooth space to improve the convergence rate. [ABSTRACT FROM AUTHOR]

If an unambiguous single-source DNA profile is obtained from a crime scene, then a potential person of interest can either match or not match the crime scene profile and the likelihood ratio for the single matching genotype can be easily computed. Mixed DNA profiles on the other hand are typically ambiguous and a vast number of different likelihood ratios can be obtained depending on the genotype of a potential person of interest that is compared with the mixture later. In the absence of a person of interest it can be unclear how suitable the profile is for discriminating between donors and non-donors. We introduce a simulation method to explore the range of likelihood ratios that is expected to be obtained when a non-donor or a true donor is compared with the mixed DNA profile. Sampling is conditional on the mixture deconvolution obtained using probabilistic genotyping. These simulations help to decide whether or not a (mixed) profile is suitable for comparison to a person of interest. Moreover, the methods can be used to determine whether a profile is suitable for upload to a database and whether or not potential rework could be advised. [ABSTRACT FROM AUTHOR]

We consider the problem of estimating the response function in a deconvolution model under fractional Gaussian noise and noisy kernel. A preliminary threshold is used to stabilize the inversion. Our estimator is adaptive and attains minimax optimal or near-optimal rates in a wide range of Besov balls. [ABSTRACT FROM AUTHOR]

This paper presents an efficient, universally stable finite-element scheme for the NSα deconvolution model. Accuracy is enhanced by van Cittert approximate deconvolution, as well as through the choice of pointwise divergence-free discrete spaces. Finite-element analysis is provided, which includes results for stability, well-posedness, and optimal convergence of both velocity and pressure solutions. Finally, several numerical experiments are presented which demonstrate the performance of NSα, as well as illustrate the advantages of pointwise divergence-free finite elements. [ABSTRACT FROM AUTHOR]

We study the heteroscedastic deconvolution problem when random noises have compactly supported densities. In this context, the Fourier transforms of the densities can vanish on the real line. We propose a truncated type of estimator for target density and derive the convergence rate of the mean L1-error uniformly over a class of target densities. A lower bound for the mean L1-error is also established. Some simulations will be given to illustrate the performance of the proposed estimator. [ABSTRACT FROM AUTHOR]

At the same total spherule volume fraction in a gaseous mainstream, we predict the significant alteration of mass deposition rate attending extensiveaggregation—illustrating our methods and results here not only for a mainstream of single-sized cluster aggregates, but also for coagulation-aged (near log-normal) distributions of large fractal-like aggregates (Ng= O(103),Df= 1.8 (DLCAs) orDf= 2.1 (RLCAs)) compared to isolated spherule depositionin the same environment. Because of their drastically different sensitivities to aggregation, we consider, sequentially, the particle transport mechanisms of either: ordinary isothermalconvective-diffusion, thermophoresis(to a cooled solid target) orinertial impaction(without rebound). Using a rather general formulation (which incorporates Knudsen transition effects expected at elevated pressures) but neglecting direct “interception” effects, we find that for, say,Df= 2.1, N = O(103),Kn1: =mfp/R1= 1, ifconvective-diffusion(with Sc >> 1) were the dominant mechanism then mainstream aggregation woulddecreaseexpected mass deposition rates to much larger targets by somewhat more than one decade. However, forthermophoresisaggregation wouldincreasedeposition rates by approximately somewhat more than one decade, and, for, say, “eddy impaction” (in a fully turbulent duct flow) aggregation wouldincreasedeposition rates by as much as nearly 1.5 decades. Physically, these large aggregation enhancement-ratios for deposition by thermophoresis or particle Inertial Impaction are attributed to drag reduction (per spherule) associated with “momentum shielding”—analogous to the aerodynamic advantages that birds, fish, bicyclists, runners,… experience when “in formation”. Using this approach, other impaction geometries and Knudsen number situations are also readily treated, as well as more “compact” even porous (Df= 3) aggregate populations. These predictive methods, illustrative results, and conclusions are expected to be useful to investigators seeking to maximize (or minimize) particle deposition rates on solid targets byexploiting control over the spherule aggregation process in the mainstream. As an important corollary, our methods also enable the quantitative deconvolution of aggregated aerosol sampling data, i.e., correcting for the systematic distortion (falsification) of sampled aggregate size distributions, pdfw(N), brought about by the size-dependent capture coefficients associated with momentum-shielding (nearly power-law: Smom∼Nk) for each of the mechanisms considered here (C-D, T-P, or E-I; Section 5)). As demonstrated in Section 6.3, while we expect Log-Normal-type distributions to retain their shape, we predict the systematic correction factors needed to obtain the mean and median aggregate sizes (andNg) that must have existed in the mainstream (see Equation (30)). These correction factors become quite significant for each of the mechanisms (especially thermophoresis and impaction) when the mainstream aggregate size-spread is large (e.g.,σg> ca. 2) and the pressure is high enough to causeKn1to drop to O(1). For completeness, the systematic consequences of the appreciable effective size ofN>> 1 cluster aggregates, briefly discussed in Section 6.2, will need to be included, especially for the deposition ofDf< 2 fractal-like aggregates on targets not much larger than the aggregates themselves (e.g., depth filter fibers,…). However, for capture by sufficiently large targets a noteworthy conclusion is that,of the distinct aerosol transport mechanisms considered here, isothermal convective-diffusion stands out as the only mechanism for which isolated spherules will deposit more efficiently than large-N cluster aggregates (when compared in the same flow environment at the same mainstream spherule volume fraction). Copyright © 2018 American Association for Aerosol Research [ABSTRACT FROM AUTHOR]

We consider the problem of multivariate density deconvolution when interest lies in estimating the distribution of a vector valued random variable X but precise measurements on X are not available, observations being contaminated by measurement errors U. The existing sparse literature on the problem assumes the density of the measurement errors to be completely known. We propose robust Bayesian semiparametric multivariate deconvolution approaches when the measurement error density of U is not known but replicated proxies are available for at least some individuals. Additionally, we allow the variability of U to depend on the associated unobserved values of X through unknown relationships, which also automatically includes the case of multivariate multiplicative measurement errors. Basic properties of finite mixture models, multivariate normal kernels, and exchangeable priors are exploited in novel ways to meet modeling and computational challenges. Theoretical results showing the flexibility of the proposed methods in capturing a wide variety of data-generating processes are provided. We illustrate the efficiency of the proposed methods in recovering the density of X through simulation experiments. The methodology is applied to estimate the joint consumption pattern of different dietary components from contaminated 24 h recalls. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

A possible modelling approach in the large eddy simulation (LES) of reactive flows is to deconvolve resolved scalars. Indeed, by inverting the LES filter, scalars such as mass fractions are reconstructed. This information can be used to close budget terms of filtered species balance equations, such as the filtered reaction rate. Being ill-posed in the mathematical sense, the problem is very sensitive to any numerical perturbation. The objective of the present study is to assess the ability of this kind of methodology to capture the chemical structure of premixed flames. For that purpose, three deconvolution methods are tested on a one-dimensional filtered laminar premixed flame configuration: the approximate deconvolution method based on Van Cittert iterative deconvolution, a Taylor decomposition-based method, and the regularised deconvolution method based on the minimisation of a quadratic criterion. These methods are then extended to the reconstruction of subgrid scale profiles. Two methodologies are proposed: the first one relies on subgrid scale interpolation of deconvolved profiles and the second uses parametric functions to describe small scales. Conducted tests analyse the ability of the method to capture the chemical filtered flame structure and front propagation speed. Results show that the deconvolution model should include information about small scales in order to regularise the filter inversion.a priorianda posterioritests showed that the filtered flame propagation speed and structure cannot be captured if the filter size is too large. [ABSTRACT FROM PUBLISHER]

The assessment of net rainfall, defined as the intermediate hydrological variable linked in between the hillslope and the river network, is a challenge. This paper presents a method for net rainfall estimation, using inverse modelling associated to a geomorphology-based transfer function. The analysis is carried out in semi-arid Tunisia, with a dataset from event discharges in a mesoscale dryland basin. A complete sensitivity analysis is developed, along with a discussion of validity limits for simplifying assumptions and the identification of paths for improvement. This work could be relevant for data-scarce areas, thanks to the use of simple dynamic conceptualization and being based on observable geomorphological features, adjusted to the available data and knowledge. [ABSTRACT FROM AUTHOR]

Pulsatile secretion of hormones in the hypothalamic-pituitary-gonadal axis is critical for normal functioning of the reproductive system. Thus, appropriate characterization of pulsatile secretion is important for identifying the (patho)physiology of reproductive conditions. Existing analysis methods often fail to adequately characterize pulsatility, especially when the signal-to-noise ratio is low. Newer Bayesian analysis methods for pulsatile hormones may offer improved secretion quantification in noisier data. The objective of this study was to extensively validate a Bayesian analysis approach for analyzing pulsatile hormones in settings that occur in reproductive studies. An investigative approach was chosen so that clinical research teams will have the knowledge to adopt this newer analysis approach in practice. Three experimental conditions were investigated: luteinizing hormone (LH) profiles in ovariectomized ewes (N=6; high signal-tonoise setting), LH profiles in young ovulating women (N=12; lower signal-to-noise setting), and computer-simulated scenarios (N=200). For each experimental condition, differences in luteinizing hormone pulse outcomes (pulse number, average pulse size, hormone half-life, and non-pulse secretion) were obtained and compared between non-Bayesian and Bayesian analysis pulse analysis methods. For the ewe model, the estimated pulse number and mass were comparable between the Bayesian and non-Bayesian analyses. For the human model, only 4 of 12 subjects could be fitted with the non-Bayesian analysis compared to 10 of the 12 with Bayesian analysis. In general, the Bayesian analysis had lower false negative rates (<4.5%) compared to the non- Bayesian analysis while maintaining a high specificity (false positive rate <2.5%). The Bayesian analysis also had less biased estimates of all pulse features. In conclusion, Bayesian analysis provides a more reliable pulse characterization in low signal-to-noise experiments and should be used for the analysis of reproductive physiology studies of pulsatile hormones. [ABSTRACT FROM AUTHOR]

This paper studies the regression estimation with errors-in-variables. We first extend Meister's theorems (Meister, 2009. Deconvolution Problems in Nonparametric Statistics. Springer, Berlin) from one to multi-dimensional setting, when a noise density has no zeros in the Fourier domain. Then motivated by the work of Delaigle and Meister (Delaigle, Meister, 2011. Nonparametric function estimation under Fourier-oscillating noise. Statistica Sinica 21, 1065-1092), we show a desired convergence rate of a kernel estimator for Fourier-oscillating noises. Finally, two technical conditions are removed, when a wavelet estimator is used. [ABSTRACT FROM AUTHOR]