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Haze and fog can significantly reduce the visibility of distant objects by scattering light and creating blurry, washed-out images lacking in detail. Image dehazing is a technique used in computer vision to enhance the clarity of such obscured images. This study examines the effectiveness of various dehazing methods using real hazy images and synthetic images with artificially created haze. Performance metrics such as PSNR, SSIM, MSE, CII, and computation time are used to evaluate the proposed method. The evaluation is carried out on datasets like RESIDE, GMAN, O-Haze, I-Haze, NH-Haze, and Dense haze to compare the proposed method with existing models. The proposed method attains 27.46%, 20.63% and 21.09% higher PSNR and 12.36%, 23.95% and 36.12% lower Natural Image Quality Evaluator for RESIDE dataset when analyzed to the existing models, such as strategic method towards contrast enhancement by 2D histogram equalization under TV decomposition (CE-TDHE-TVD), multiple level framework basis contrast enhancement for uniform with non-uniform back ground imageries utilizing appropriate histogram equalization (CE-VHE), and Contrast enhancement with brightness preservation of low light pictures with the help of combined CLAHE and BPDHE histogram equalization (CE-CLAHE-BPDHE) respectively. [ABSTRACT FROM AUTHOR]

Stripe noise remains a significant source of errors and image quality degradation in remote sensing systems. A prominent approach for tackling this problem is the first-order Total Variation (TV) regularization, which has a proven efficiency in dealing with stripe noise. Unfortunately, denoised images, in this case, may suffer from texture loss and staircase artefacts around smooth areas. In this paper, a novel image decomposition scheme is proposed to tackle these drawbacks. This decomposition is based on the use of directional first- and second-order TV regularizers that are employed to separate the clear image from the stripe component while considering the directionality and smoothness of the latter. The proposed model is solved using a Chambolle-based algorithm and its performance is compared to traditional destriping methods using different noise structures and intensities. The results have shown comparable performance to the existing state-of-the-art methods with some improvements in structure preservation and noise cancellation. [ABSTRACT FROM AUTHOR]

Hyperspectral band selection plays a key role in reducing the high dimensionality of data while maintaining essential details. However, existing band selection methods often encounter challenges, such as high memory consumption, the need for data matricization that disrupts inherent data structures, and difficulties in preserving crucial spatial–spectral relationships. To address these challenges, we propose a tensor-based band selection model using Generalized 3D Total Variation (G3DTV), which utilizes the ℓ 1 p norm to promote smoothness across spatial and spectral dimensions. Based on the Alternating Direction Method of Multipliers (ADMM), we develop an efficient hyperspectral band selection algorithm, where the tensor low-rank structure is captured through tensor CUR decomposition, thus significantly improving computational efficiency. Numerical experiments on benchmark datasets have demonstrated that our method outperforms other state-of-the-art approaches. In addition, we provide practical guidelines for parameter tuning in both noise-free and noisy data scenarios. We also discuss computational complexity trade-offs, explore parameter selection using grid search and Bayesian Optimization, and extend our analysis to evaluate performance with additional classifiers. These results further validate the proposed robustness and accuracy of the model. [ABSTRACT FROM AUTHOR]

Unsupervised learning models, particularly in the remote sensing domain, have gained significant attention in recent years. Various degradations in the satellite images, primarily occurring during acquisition, pose a substantial hurdle in obtaining reliable ground truth and extensive training data. The Deep Image Prior model (DIP) addresses these issues by performing restoration tasks using a single image, relying on the implicit regularization inherent in the network architecture. In this paper, we propose a novel approach, integrating the DIP model within the retinex framework to restore aerial and satellite images from the Gamma distributed speckles and linear shift-invariant Gaussian blur along with contrast enhancement using the alternating proximal gradient descent ascent (PGDA) method. Our proposed methodology combines implicit regularization with explicit total variational (TV) regularization, incorporating automated estimation of local regularization parameters. The data-fidelity component in the optimization function is formulated using the Bayesian Maximum A posteriori (MAP) estimate, assuming the speckles follow the Gamma distribution. Demonstration of despeckling and deblurring alone and in addition as a combined task is carried out on aerial and Synthetic Aperture Radar (SAR) images with different resolutions and polarization from various sources. Results obtained are compared with various state-of-the-art despeckling and deblurring models using distinct image quality metrics such as Equivalent Number of Looks (ENL), Contrast to Noise Ratio (CNR), Edge Preserving Index (EPI), Entropy, Global Contrast Factor (GCF), Natural Image Quality Evaluator (NIQE), Blind/Referenceless Image Spatial Quality Evaluator (BRISQUE) and Bradley-Terry (B-T) score based on the various factors. The quality of restored images depicted superior performance of the proposed method over the existing models under study. [ABSTRACT FROM AUTHOR]

Objective. Accurate image reconstruction from data with truncation in x-ray computed tomography (CT) remains a topic of research interest; and the works reported previously in the literature focus largely on reconstructing an image only within the scanning field-of-view (FOV). We develop algorithms to invert the truncated data model for numerically accurate image reconstruction within the subject support or a region slightly smaller than the subject support. Methods. We formulate image reconstruction from data with truncation as an optimization program, which includes hybrid constraints on region-based image total-variation (TV) and image ℓ 1 -norm (L1) for effectively suppressing truncation artifacts. An algorithm, referred to as the TV-L1 algorithm, is developed for image reconstruction (i.e. inversion of the data model) from data with truncation through solving the optimization program. Results. We perform numerical studies to evaluate accuracy and stability of the TV-L1 algorithm by using simulated and real CT data. Accurate images can be obtained stably by use of the TV-L1 algorithm within the subject support, or a region substantially larger than the FOV, from data with truncation of varying degrees. Conclusions. The TV-L1 algorithm can invert the truncated data model to accurately and stably reconstruct images within the subject support, or a region slightly smaller than the subject support but substantially larger than the FOV. Significance. Accurate image reconstruction within the subject support, or a region substantially larger than the FOV, from data with truncation can be of theoretical and practical implication. The insights and TV-L1 algorithm may also be generalized to accurate image reconstruction from data with truncation in other tomographic imaging modalities. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new nonlocal model that uses a weighted difference of anisotropic and isotropic total variation (TV) to regularize the partition boundaries in an image. The proposed model integrates the nonlocal operators with the weighted differences of two convex terms, which can exploit the variety nature of textured images to recover all important features and fine detail structures. To solve our proposed model, we apply the difference of convex algorithm (DCA). Then, the subproblems can be minimized by the split-Bregman iteration method introduced in Goldstein and Osher (2009) combined with the Bregmanized Operator Splitting (BOS) method introduced in Zhang et al. (2010). We prove that the sequence generated by the DCA method converges to a stationary point, which satisfies the first-order optimality condition. Various experiments show that the proposed model yields results that can compare favorably with those obtained by various methods in the literature. [ABSTRACT FROM AUTHOR]

This study introduces a novel compound regularization technique for Elastic Impedance (EI) inversion that combines Total Variation (TV1) and Total Variation of the second-order (TV2) regularizations. This method leverages the Split-Bregman algorithm to effectively address the staircase effect, a common limitation of using TV1 regularization alone. The proposed approach enforces smoothness (TV1) and improved edge preservation (TV2) in the reconstructed EI models, leading to more accurate representations. The efficacy of this method is demonstrated by applying it to two geologically relevant elastic models: the Marmousi model (complex but synthetic) and seismic field data from the Gulf of Mexico. Numerical tests were conducted using realistic noise levels, and the results confirmed the proposed method's ability to reconstruct detailed and accurate EI models for both models, highlighting its generalizability to diverse geological scenarios. Unlike the simpler TV1 and TV2 regularizations, our combined approach adeptly handles complex models featuring both smooth and abrupt transitions, though its performance can vary across different geological scenarios. This method provides a promising framework for improved EI reconstruction in diverse geological settings. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel curvature-guided saturation-value total variation model for color image restoration. Specifically, we incorporate the curvature prior into the traditional variational model to guide the evolution in the direction that maintains the curvature information. Theoretically, we investigate the properties of the proposed model and give a detailed discussion based on the mathematical foundation about the existence of the solution. Numerically, we formulate an effective and efficient algorithm to solve the proposed minimization problem based on the framework of alternating direction method of multipliers. Numerical examples are presented to demonstrate that the performance of the proposed model is better than that of other testing methods for several testing color images. [ABSTRACT FROM AUTHOR]

Background: Irregular cardiac motion can render conventional segmented cine MRI nondiagnostic. Clustering has been proposed for cardiac motion binning and may be optimized for complex arrhythmias. Purpose: To develop an adaptive cluster optimization method for irregular cardiac motion, and to generate the corresponding time‐resolved cine images. Study Type: Prospective. Subjects: Thirteen with atrial fibrillation, four with premature ventricular contractions, and one patient in sinus rhythm. Field Strength/Sequence: Free‐running balanced steady state free precession (bSSFP) with sorted golden‐step, reference real‐time sequence. Assessment: Each subject underwent both the sorted golden‐step bSSFP and the reference Cartesian real‐time imaging. Golden‐step bSSFP images were reconstructed using the dynamic regularized adaptive cluster optimization (DRACO) method and k‐means clustering. Image quality (4‐point Likert scale), signal‐to‐noise ratio (SNR), contrast‐to‐noise ratio (CNR), edge sharpness, and ventricular function were assessed. Statistical Tests: Paired t‐tests, Friedman test, regression analysis, Fleiss' Kappa, Bland–Altman analysis. Significance level P < 0.05. Results: The DRACO method had the highest percent of images with scores ≥3 (96% for diastolic frame, 93% for systolic frame, and 93% for multiphase cine) and the percentages were significantly higher compared with both the k‐means and real‐time methods. Image quality scores, SNR, and CNR were significantly different between DRACO vs. k‐means and between DRACO vs. real‐time. Cardiac function analysis showed no significant differences between DRACO vs. the reference real‐time. Conclusion: DRACO with time‐resolved reconstruction generated high quality images and has early promise for quantitative cine cardiac MRI in patients with complex arrhythmias including atrial fibrillation. Level of Evidence: 1. Technical Efficacy: Stage 2. [ABSTRACT FROM AUTHOR]

Purpose: The structural similarity index measure (SSIM) has become a popular quality metric to evaluate QSM in a way that is closer to human perception than RMS error (RMSE). However, SSIM may overpenalize errors in diamagnetic tissues and underpenalize them in paramagnetic tissues, resulting in biasing. In addition, extreme artifacts may compress the dynamic range, resulting in unrealistically high SSIM scores (hacking). To overcome biasing and hacking, we propose XSIM: SSIM implemented in the native QSM range, and with internal parameters optimized for QSM. Methods: We used forward simulations from a COSMOS ground‐truth brain susceptibility map included in the 2016 QSM Reconstruction Challenge to investigate the effect of QSM reconstruction errors on the SSIM, XSIM, and RMSE metrics. We also used these metrics to optimize QSM reconstructions of the in vivo challenge data set. We repeated this experiment with the QSM abdominal phantom. To validate the use of XSIM instead of SSIM for QSM quality assessment across a range of different reconstruction techniques/algorithms, we analyzed the reconstructions submitted to the 2019 QSM Reconstruction Challenge 2.0. Results: Our experiments confirmed the biasing and hacking effects on the SSIM metric applied to QSM. The XSIM metric was robust to those effects, penalizing the presence of streaking artifacts and reconstruction errors. Using XSIM to optimize QSM reconstruction regularization weights returned less overregularization than SSIM and RMSE. Conclusion: XSIM is recommended over traditional SSIM to evaluate QSM reconstructions against a known ground truth, as it avoids biasing and hacking effects and provides a larger dynamic range of scores. [ABSTRACT FROM AUTHOR]

Solving total variation problems is fundamentally important for many computer vision tasks, such as image smoothing, optical flow estimation and 3D surface reconstruction. However, the traditional iterative solvers require a large number of iterations to converge, while deep learning solvers have a huge number of parameters, hampering their practical deployment. To address these issues, this paper first introduces a novel iterative algorithm that is 6 ~ 75 times faster than previous iterative methods. The proposed iterative method converges and converges to the optimal solution. These two facts are theoretically guaranteed and numerically confirmed, respectively. Then, we generalize this algorithm to a compact implicit neural network that has only 0.003M parameters. The network is shown to be more effective and efficient. Thanks to the small number of parameters, the proposed network can be applied in a wide range of applications where total variation is imposed. The source code for the iterative solver and the neural network is publicly available at https://github.com/gyh8/IRS.

In this paper, an Ordered Subsets Expectation Maximization (OSEM) reconstruction algorithm based on Total Variation (TV) constraint was applied for sparse reconstruction of X-ray fluorescence CT. First, the Geant4 Monte Carlo code was used to simulate the imaging process of fan beam X-ray fluorescence CT imaging system based on parallel hole collimator. Then, the reconstructed image quality of the proposed algorithm with varying numbers of projections was evaluated using RMSE and CNR. Finally, the relationship between the number of subsets of the algorithm and the quality of the reconstructed image and the reconstruction time was explored. The results demonstrated that, compared with the conventional OSEM algorithm, the proposed OSEM algorithm based on Total Variation constraint has higher quality of reconstructed images at different projection numbers, and the reconstruction time of the algorithm decreases with the increase of subset, which achieves the purpose of improving the quality of the reconstructed image and reducing the reconstruction time when sparse reconstruction.

Due to their ability to handle discontinuous images while having a well-understood behavior, regularizations with total variation (TV) and total generalized variation (TGV) are some of the best-known methods in image denoising. However, like other variational models including a fidelity term, they crucially depend on the choice of their tuning parameters. A remedy is to choose these automatically through multilevel approaches, for example by optimizing performance on noisy/clean image pairs. In this work, we consider such methods with space-dependent parameters which are piecewise constant on dyadic grids, with the grid itself being part of the minimization. We prove existence of minimizers for fixed discontinuous parameters under mild assumptions on the data, which lead to existence of finite optimal partitions. We further establish that these assumptions are equivalent to the commonly used box constraints on the parameters. On the numerical side, we consider a simple subdivision scheme for optimal partitions built on top of any other bilevel optimization method for scalar parameters, and demonstrate its improved performance on some representative test images when compared with constant optimized parameters. [ABSTRACT FROM AUTHOR]

In this paper, we show that for an Sp(k + 1)-invariant metric ĝ on S 4 k + 3 (k ⩾ 1) close to the round metric, the conformally compact Einstein (CCE) manifold (M, g) with (S 4 k + 3 , [ g ^ ]) as its conformai infinity is unique up to isometry. Moreover, by the result in Li et al. (2017), g is the Graham-Lee metric (see Graham and Lee (1991)) on the unit ball B1 ⊂ ℝ4k+4. We also give an a priori estimate of the Einstein metric g. As a by-product of the a priori estimates, based on the estimate and Graham-Lee and Lee's seminal perturbation results (see Graham and Lee (1991) and Lee (2006)), we directly use the continuity method to obtain an existence result of the non-positively curved CCE metric with prescribed conformal infinity (S 4 k + 3 , [ g ^ ]) when the metric ĝ is Sp(k + 1)-invariant. We also generalize the results to the case of conformal infinity (S 15 , [ g ^ ]) with ĝ a Spin(9)-invariant metric in the appendix. [ABSTRACT FROM AUTHOR]

Image labeling and graph partitioning aim to divide a set of pixels or vertices into a specific number of meaningful groups. In this paper, we propose effective truncated regularization methods for both image labeling and graph partitioning problems. More specifically, we present optimization models for piecewise constant and piecewise smooth image labeling that minimize the truncation of different potential functions. The efficient alternating direction method of multipliers based algorithm is put forward for solving these models, where all subproblems can be solved by the closed-form solution or fast Fourier transform. Moreover, we propose a semi-supervised graph partitioning model based on truncated regularization under the definition of the graph, which is solved by the proximal gradient method. The efficiency of the proposed methods is demonstrated through labeling results on synthetic and real images and semi-supervised partitioning results on graph data. [ABSTRACT FROM AUTHOR]

We consider the inverse conductivity problem with discontinuous conductivities. We show in a rigorous way, by a convergence analysis, that one can construct a completely discrete minimization problem whose solution is a good approximation of a solution to the inverse problem. The minimization problem contains a regularization term which is given by a total variation penalization and is characterized by a regularization parameter. The discretization involves at the same time the boundary measurements, by the use of the complete electrode model, the unknown conductivity and the solution to the direct problem. The electrodes are characterized by a parameter related to their size, which in turn controls the number of electrodes to be used. The discretization of the unknown and of the solution to the direct problem is characterized by another parameter related to the size of the mesh involved. In our analysis we show how to precisely choose the regularization, electrodes size and mesh size parameters with respect to the noise level in such a way that the solution to the discrete regularized problem is meaningful. In particular we obtain that the electrodes and mesh size parameters should decay polynomially with respect to the noise level. [ABSTRACT FROM AUTHOR]

BACKGROUND AND OBJECTIVE: Optimization based image reconstruction algorithm is an advanced algorithm in medical imaging. However, the corresponding solving algorithm is challenging because the model is usually large-scale and non-smooth. This work aims to devise a simple and convergent solver for optimization model. METHODS: The alternating direction method of multipliers (ADMM) algorithm is a simple and effective solver of the optimization model. However, there always exists a sub-problem that has not close-form solution. One may use gradient descent algorithm to solve this sub-problem, but the step-size selection via line search is time-consuming. Or, one may use fast Fourier transform (FFT) to get a close-form solution if the sparse transform matrix is of special structure. In this work, we propose a fully linearized ADMM (FL-ADMM) algorithm that avoids line search to determine step-size and applies to sparse transform of any structure. RESULTS: We derive the FL-ADMM algorithm instances for three total variation (TV) models in 2D computed tomography (CT). Further, we validate and evaluate one FL-ADMM algorithm and explore how two important factors impact convergence rate. These studies show that the FL-ADMM algorithm may accurately solve the optimization model. CONCLUSION: The FL-ADMM algorithm is a simple, effective, convergent and universal solver of optimization model in image reconstruction. Compared to the standard ADMM algorithm, the new algorithm does not need time-consuming step-size line-search or special demand to sparse transform. It is a rapid prototyping tool for optimization based image reconstruction. [ABSTRACT FROM AUTHOR]

Stripe noise removal is a fundamental task in remote sensing image processing, which is of great significance in improving image quality and subsequent applications. The standard nuclear norm has been widely used to remove stripe noises, but it treats each singular value equally and affects its capability and flexibility in destriping. In this paper, we proposed a weighted low-rank spatial-spectral total variation (WLRSSTV) model by exploiting the weighted nuclear norm and global spatial-spectral total variation regularization. The split Bregman iteration is used to optimize the WLRSSTV model and to estimate the weight of the nuclear norm. Extensive experiments on both the synthetic and real remote sensing images validate that the proposed model can effectively remove the stripe noise and preserve more fine-scale details. [ABSTRACT FROM AUTHOR]

This paper reports on our study of a regularization path algorithm for a regression spline estimator based on B-splines and total variation penalty. The total variation-penalized regression spline estimation method enjoys a spatial adaptation property, since the penalty function enables data-adaptive knot selection. Although the theoretical properties of the related methods have been well established in the literature, the existing implementation algorithms are usually based on techniques with a high computational cost. In particular, the selection of the optimal complexity parameter, required to strike a balance in bias-variance tradeoff, is based on the computationally intensive grid search method. In this study, we propose an efficient path algorithm by formulating an equivalent ℓ 1 penalized optimization problem. The least angle regression algorithm is applied to the reformulated problem to obtain an entire path of the jump size of B-spline derivatives that represents the knot removal condition. Numerical studies based on real and simulated data are provided to illustrate the advantages of the proposed algorithm. The simulation result shows that the proposed algorithm is significantly faster than an existing algorithm. The proposed algorithm has an additional benefit of obtaining an entire regularization path, which can provide additional statistical insights into the given problem. [ABSTRACT FROM AUTHOR]

In X-ray CT imaging, there are some cases where the obtained CT images have serious ring artifacts and noise, and these degraded CT images seriously affect the quality of clinical diagnosis. Thus, developing an effective method that can simultaneously suppress ring artifacts and noise is of great importance. Total variation (TV) is a famous prior regularization for image denoising in the image processing field, however, for degraded CT images, it can suppress the noise but fail to reduce the ring artifacts. To address this issue, the L 0 smoothing filter is incorporated with TV prior for CT ring artifacts and noise removal problem where the problem is transformed into several optimization sub-problems which are iteratively solved. The experiments demonstrate that the ring artifacts and noise presented in the CT image can be effectively suppressed by the proposed method and meanwhile the detailed features such as edge structure can be well preserved. As the superiority of TV and L 0 smoothing filters are fully utilized, the performance of the proposed method is better than the existing methods such as the TV-based method and L 0 -based method. [ABSTRACT FROM AUTHOR]

The present work intends to compare two statistical classification methods using images as covariates and under the comparison criterion of the ROC curve. The first implemented procedure is based on exploring a mathematical-statistical model using multidimensional arrangements, frequently known as tensors. It is based on the theoretical framework of the high-dimensional generalized linear model. The second methodology is situated in the field of functional data analysis, particularly in the space of functions that have a finite measure of the total variation. A simulation study is carried out to compare both classification methodologies using the area under the ROC curve (AUC). The model based on functional data had better performance than the tensor model. A real data application using medical images is presented. [ABSTRACT FROM AUTHOR]

In this paper, we study a three dimensional model for grain boundary motion with the presence of time-dependent external forces. We show existence of solutions in the large. We also show that the ω-limit set of the solutions is compact and that the ω-limit points satisfy the corresponding elliptic system. In the case of no external forcing for the rotation and, under a condition on the range of the initial datum, we prove that the system reaches a steady state in a finite time and that, in this case, the rotation becomes a constant one. [ABSTRACT FROM AUTHOR]

Loss functions are an essential part in modern data-driven approaches, such as bi-level training scheme and machine learnings. In this paper, we propose a loss function consisting of a r -order (an)-isotropic total variation semi-norms TV r , r ∈ ℝ + , defined via the Riemann–Liouville (RL) fractional derivative. We focus on studying key theoretical properties, such as the lower semi-continuity and compactness with respect to both the function and the order of derivative r , of such loss functions. [ABSTRACT FROM AUTHOR]

We study the BMO-type functional \kappa _{\varepsilon }(f,\mathbb {R}^n), which can be used to characterize bounded variation functions f\in \mathrm {BV}(\mathbb {R}^n). The \Gamma-limit of this functional, taken with respect to L^1_{\mathrm {loc}}-convergence, is known to be \tfrac 14 |Df|(\mathbb {R}^n). We show that the \Gamma-limit with respect to L^{\infty }_{\mathrm {loc}}-convergence is \[ \tfrac 14 |D^a f|(\mathbb {R}^n)+\tfrac 14 |D^c f|(\mathbb {R}^n)+\tfrac 12 |D^j f|(\mathbb {R}^n), \] which agrees with the "pointwise" limit in the case of special functions of bounded varation. [ABSTRACT FROM AUTHOR]

Multiplicative noise removal problems have attracted much attention in recent years. Unlike additive noise, multiplicative noise destroys almost all information of the original image, especially for texture images. Motivated by the TV-Stokes model, we propose a new two-step variational model to denoise the texture images corrupted by multiplicative noise with a good geometry explanation in this paper. In the first step, we convert the multiplicative denoising problem into an additive one by the logarithm transform and propagate the isophote directions in the tangential field smoothing. Once the isophote directions are constructed, an image is restored to fit the constructed directions in the second step. The existence and uniqueness of the solution to the variational problems are proved. In these two steps, we use the gradient descent method and construct finite difference schemes to solve the problems. Especially, the augmented Lagrangian method and the fast Fourier transform are adopted to accelerate the calculation. Experimental results show that the proposed model can remove the multiplicative noise efficiently and protect the texture well. [ABSTRACT FROM AUTHOR]

Image deblurring is one of the most fundamental problems in the image processing and computer vision fields. The methods based on total variation are effective for image deblurring because it is able to preserve sharp edges, which are usually the most important parts of an image. However, these methods usually produce undesirable staircase artifacts. In order to alleviate the staircase effects, in this paper we propose an effective scheme for image deblurring based on the TVp regularization and wavelet frame. The new model combines the advantages of nonconvex regularization and wavelet frame based method, and it can well remove the blur and noise while preserving the valuable edges and contours of the image. To solve the proposed model, we develop a fast minimization algorithm under the framework of the split Bregman algorithm and further apply Nesterov acceleration technique to improve the convergence speed. The results from peak signal-to-noise ratio and structural similarity index measurements show the effectiveness of our proposed method when compared to previous state-of-the-art methods for image deblurring. [ABSTRACT FROM AUTHOR]

• Double bias fields are introduced into fidelity term to approximate image intensity inhomogeneity. • The proposed energy function is strictly convex, and allows flexible initialization. • A TV (total variation) regularization term is introduced to keep convex level-set function smooth. • The proposed method is robust against to noise and intensity inhomogeneity. The existing active contour models (ACMs) based on bias field (BF) correction mostly rely on a single BF assumption and lack in-depth discussion on the convexity of the energy functional, often leading to the problem of local minima. To address this issue, this paper introduces a dual BF and proposes a convex level-set (LS) method based on multiplicative-additive (MA) model to achieve global minima. Firstly, a MA model is adopted as the fidelity term, and a kernel function is introduced to adjust the size of the intensity inhomogeneous neighborhood, enhancing the adaptability to intensity inhomogeneity. Then, the convex LS function is embedded in the variational framework to ensure convexity of each variable in the energy functional. This transformation turns the segmentation problem into a convex optimization problem. By introducing the total variation regularization term to smooth the LS function, the model's resistance to noise is effectively enhanced. Finally, by minimizing the proposed energy functional, image segmentation and BF correction are successfully achieved. Experimental results validate the global minima property of our model, while also demonstrating good flexibility in the initial contour. The proposed model achieves superior segmentation results compared to other classical ACMs on various types of images. [ABSTRACT FROM AUTHOR]

This article presents a novel approach to image restoration utilizing a unique non-convex l 1 / 2 -TV regularization model. This model integrates the l 1 / 2 -quasi norm as a regularization function, introducing non-convexity to promote sparsity and unevenly penalize elements, thereby enhancing restoration outcomes. To tackle this model, an efficient algorithm named the Alternating Direction Method of Multipliers, based on the Lagrangian multiplier, is introduced. This effectively prevents the penalty parameter from reaching infinity and ensures excellent convergence behavior. The proposed algorithm decomposes the optimization problem into subproblems, for which closed-form solutions are derived, particularly addressing the challenging l 1 / 2 regularization problem. To validate its effectiveness, a comprehensive set of experiments are conducted to compare its performance with existing methods. The experimental results demonstrate that the proposed model performs well in both qualitative and quantitative evaluations. Consequently, the proposed model is not only efficient and stable but also exhibits excellent convergence behavior. • A novel regularization model for image restoration, based on non-convex total variation is proposed in this work. • We propose an effective solution approach to solve the model using the Alternating Direction Method of Multipliers (ADMM). • The proposed solution provides the closed-form thresholding formula for regularization model. • Extensive numerical experiments demonstrate the superiority of the proposed method over compared methods. [ABSTRACT FROM AUTHOR]

Model-based hyperspectral image (HSI) denoising methods have attracted continuous attention in the past decades, due to their effectiveness and interpretability. In this work, we aim at advancing model-based HSI denoising, through sophisticated investigation for both the fidelity and regularization terms, or correspondingly noise and prior, by virtue of several recently developed techniques. Specifically, we formulate a novel unified probabilistic model for the HSI denoising task, within which the noise is assumed as pixel-wise non-independent and identically distributed (non-i.i.d) Gaussian predicted by a pre-trained neural network, and the prior for the HSI image is designed by incorporating the deep image prior (DIP) with total variation (TV) and spatio-spectral TV. To solve the resulted maximum a posteriori (MAP) estimation problem, we design a Monte Carlo Expectation–Maximization (MCEM) algorithm, in which the stochastic gradient Langevin dynamics (SGLD) method is used for computing the E-step, and the alternative direction method of multipliers (ADMM) is adopted for solving the optimization in the M-step. Experiments on both synthetic and real noisy HSI datasets have been conducted to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, utilizing the quadratic penalty technique and adding a proximal term in one subproblem, we propose the proximal alternating minimization method for solving Poisson noise removal problem. For the fixed parameters, the convergence of proximal alternating algorithm is established under very mild conditions. In order to accelerate the proposed proximal algorithm, the variable stepsize, that is like Barzilai-Borwein stepsize, is applied to the proximal parameter. Compared with several state-of-the-arts algorithms, numerical results demonstrate the superiority of the new approach. [ABSTRACT FROM AUTHOR]

Objectives: Magnetic resonance imaging (MRI) is a commonly used tool in clinical medicine, but it suffers from the disadvantage of slow imaging speed. To address this, we propose a novel MRI reconstruction algorithm based on image decomposition to realize accurate image reconstruction with undersampled k‐space data. Methods: In our algorithm, the MR images to be recovered are split into cartoon and texture components utilizing image decomposition theory. Different sparse transform constraints are applied to each component based on their morphological structure characteristics. The total variation transform constraint is used for the smooth cartoon component, while the L0 norm constraint of tight frame redundant transform is used for the oscillatory texture component. Finally, an alternating iterative minimization approach is adopted to complete the reconstruction. Results: Numerous numerical experiments are conducted on several MR images and the results consistently show that, compared with the existing classical compressed sensing algorithm, our algorithm significantly improves the peak signal‐to‐noise ratio of the reconstructed images and preserves more image details. Conclusions: Our algorithm harnesses the sparse characteristics of different image components to reconstruct MR images accurately with highly undersampled data. It can greatly accelerate MRI speed and be extended to other imaging reconstruction fields. [ABSTRACT FROM AUTHOR]

We give a complete characterization of all real-valued functions on the unit circle \(S^1\) that can be represented by integrating the spherical distance on \(S^1\) with respect to a signed measure or a probability measure. [ABSTRACT FROM AUTHOR]

Background: Angiography is a medical imaging technique that uses X-ray imaging to visualize blood vessels in the body, aiding in the diagnosis of vascular conditions. Coronary angiography is a vital medical procedure that provides detailed images of a patient's coronary arteries and helps diagnose heart-related conditions. Challenges in coronary angiography involve image noise, which can reduce image quality and make it difficult to identify vascular structures. Additionally, variations in contrast and the presence of artifacts can impact the accuracy of diagnoses. To improve the image quality and enhance the image visibility needed to address the above challenges, this article proposed a novel hybrid approach called the Mean Total Variation Filter (MTVF). Materials & Methods: The study used an experimental design to assess how well the Mean Total Variation Filter (MTVF) improves the quality of coronary angiography images. The medical images were obtained in a controlled lab setting, where the research was carried out and the subsequent analysis was performed. The study spanned approximately six months, covering the phases of developing the algorithm, acquiring images, and evaluating performance. To select images, a purposive sampling method was employed, focusing on coronary angiography images with various levels of noise and artifacts. This method ensures that the selected images represent common challenges found in clinical practice. Preliminary studies suggested a minimum of 30 images were needed to achieve statistically significant results, ensuring enough test cases to accurately evaluate the proposed algorithm's performance. The effectiveness of the MTVF approach was measured using several quantitative metrics: Correlation Coefficient (CoC), Peak Signal-to-Noise Ratio (PSNR), Mean Square Error (MSE), and Root Mean Square Error (RMSE). These metrics were chosen to thoroughly assess the algorithm's capability in reducing noise and enhancing image quality. Results: The performance of the proposed algorithm was assessed using various parameters for test image 1. The evaluation results indicate a high CoC of 0.9997, an impressive PSNR of 51.01, a low MSE of 1.3020, and a minimal RMSE of 0.0133. These metrics collectively highlight the algorithm's ability to produce excellent results in enhancing the quality of test image 1, making it a promising technique for noise reduction and image enhancement. Conclusion: The analysis highlights the outstanding performance of the proposed hybrid MTVF method in removing noise, outperforming current techniques. [ABSTRACT FROM AUTHOR]

We study stability and inclusion of the jump set of minimizers of convex denoising functionals, such as the celebrated "Rudin-Osher-Fatemi" functional, for scalar or vectorial signals. We show that under mild regularity assumptions on the data fidelity term and the regularizer, the jump set of the minimizer is essentially a subset of the original jump set. Moreover, we give an estimate on the magnitude of the jumps in terms of the data. This extends old results, in particular of the first author (with Caselles and Novaga) and of Valkonen, to much more general cases. We also consider the case where the original datum has unbounded variation, and we define a notion of its jump set which, again, must contain the jump set of the solution. [ABSTRACT FROM AUTHOR]

In this study, we develop a nonmonotone variable metric Barzilai-Borwein method for minimizing the sum of a smooth function and a convex, possibly nondifferentiable, function. At each step, the descent direction is obtained by taking the difference between the minimizer of the scaling proximal function and the current iteration point. An adaptive nonmonotone line search is proposed for determining the step length along this direction. We also show that the limit point of the iterates sequence is a stationary point. Numerical results with parallel magnetic resonance imaging, Poisson, and Cauchy noise deblurring demonstrate the effectiveness of the new algorithm.

The acquisition time of magnetic resonance imaging (MRI) is relatively long. To achieve high-quality and fast reconstruction of magnetic resonance (MR) images, we proposed a non-convex regularization model for MR image reconstruction with the modified transformed $ {l_1} $ total variation (MTL1TV) regularization term. We addressed this new model using the alternating direction method of multipliers (ADMM). To evaluate the proposed MTL1TV model, we performed numerical experiments on several MR images. The numerical results showed that the proposed model gives reconstructed images of improved quality compared with those obtained from state of the art models. The results indicated that the proposed model can effectively reconstruct MR images.