Total Variation Penalty Research Articles

Forward and Inverse Modeling of Depth-of-Field Effects in Background-Oriented Schlieren

This paper reports a novel cone-ray model of background-oriented schlieren (BOS) imaging that accounts for depth-of-field effects. Reconstructions of the density field performed with this model are far more robust to the blur associated with a finite aperture than conventional reconstructions, which presume a thin-ray pinhole camera. Our model is characterized and validated using forward evaluations of simulated buoyancy-driven flow and both simulated and experimental BOS measurements of hypersonic flow over a sphere. Moreover, the model is embedded in a neural reconstruction algorithm, which is demonstrated with a total variation penalty and the compressible Euler equations. Our cone-ray technique dramatically improves the accuracy of BOS reconstructions: the shock interface is well-resolved in all our tests, irrespective of the camera’s aperture setting, which spans f-numbers from 22 down to 4.

A graph decomposition-based approach for the graph-fused lasso

We propose a new algorithm for solving the graph-fused lasso (GFL), a regularized model that operates under the assumption that the signal tends to be locally constant over a predefined graph structure. The proposed method applies a novel decomposition of the objective function for the alternating direction method of multipliers (ADMM) algorithm. While ADMM has been widely used in fused lasso problems, existing works such as the network lasso decompose the objective function into the loss function component and the total variation penalty component. In contrast, based on the graph matching technique in graph theory, we propose a new method of decomposition that separates the objective function into two components, where one component is the loss function plus part of the total variation penalty, and the other component is the remaining total variation penalty. We develop an exact convergence rate of the proposed algorithm by developing a general theory on the local convergence of ADMM. Compared with the network lasso algorithm, our algorithm has a faster exact linear convergence rate (although in the same order as for the network lasso). It also enjoys a smaller computational cost per iteration, thus converges overall faster in most numerical examples.

TENSOR QUANTILE REGRESSION WITH LOW-RANK TENSOR TRAIN ESTIMATION.

Neuroimaging studies often involve predicting a scalar outcome from an array of images collectively called tensor. The use of magnetic resonance imaging (MRI) provides a unique opportunity to investigate the structures of the brain. To learn the association between MRI images and human intelligence, we formulate a scalar-on-image quantile regression framework. However, the high dimensionality of the tensor makes estimating the coefficients for all elements computationally challenging. To address this, we propose a low-rank coefficient array estimation algorithm based on tensor train (TT) decomposition which we demonstrate can effectively reduce the dimensionality of the coefficient tensor to a feasible level while ensuring adequacy to the data. Our method is more stable and efficient compared to the commonly used, Canonic Polyadic rank approximation-based method. We also propose a generalized Lasso penalty on the coefficient tensor to take advantage of the spatial structure of the tensor, further reduce the dimensionality of the coefficient tensor, and improve the interpretability of the model. The consistency and asymptotic normality of the TT estimator are established under some mild conditions on the covariates and random errors in quantile regression models. The rate of convergence is obtained with regularization under the total variation penalty. Extensive numerical studies, including both synthetic and real MRI imaging data, are conducted to examine the empirical performance of the proposed method and its competitors.

Iterative image reconstruction algorithm analysis for optical CT radiochromic gel dosimetry

Background. Modern radiation therapy technologies aim to enhance radiation dose precision to the tumor and utilize hypofractionated treatment regimens. Verifying the dose distributions associated with these advanced radiation therapy treatments remains an active research area due to the complexity of delivery systems and the lack of suitable three-dimensional dosimetry tools. Gel dosimeters are a potential tool for measuring these complex dose distributions. A prototype tabletop solid-tank fan-beam optical CT scanner for readout of gel dosimeters was recently developed. This scanner does not have a straight raypath from source to detector, thus images cannot be reconstructed using filtered backprojection (FBP) and iterative techniques are required. Purpose. To compare a subset of the top performing algorithms in terms of image quality and quantitatively determine the optimal algorithm while accounting for refraction within the optical CT system. The following algorithms were compared: Landweber, superiorized Landweber with the fast gradient projection perturbation routine (S-LAND-FGP), the fast iterative shrinkage/thresholding algorithm with total variation penalty term (FISTA-TV), a monotone version of FISTA-TV (MFISTA-TV), superiorized conjugate gradient with the nonascending perturbation routine (S-CG-NA), superiorized conjugate gradient with the fast gradient projection perturbation routine (S-CG-FGP), superiorized conjugate gradient with with two iterations of CG performed on the current iterate and the nonascending perturbation routine (S-CG-2-NA). Methods. A ray tracing simulator was developed to track the path of light rays as they traverse the different mediums of the optical CT scanner. Two clinical phantoms and several synthetic phantoms were produced and used to evaluate the reconstruction techniques under known conditions. Reconstructed images were analyzed in terms of spatial resolution, signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), signal non-uniformity (SNU), mean relative difference (MRD) and reconstruction time. We developed an image quality based method to find the optimal stopping iteration window for each algorithm. Imaging data from the prototype optical CT scanner was reconstructed and analysed to determine the optimal algorithm for this application. Results. The optimal algorithms found through the quantitative scoring metric were FISTA-TV and S-CG-2-NA. MFISTA-TV was found to behave almost identically to FISTA-TV however MFISTA-TV was unable to resolve some of the synthetic phantoms. S-CG-NA showed extreme fluctuations in the SNR and CNR values. S-CG-FGP had large fluctuations in the SNR and CNR values and the algorithm has less noise reduction than FISTA-TV and worse spatial resolution than S-CG-2-NA. S-LAND-FGP had many of the same characteristics as FISTA-TV; high noise reduction and stability from over iterating. However, S-LAND-FGP has worse SNR, CNR and SNU values as well as longer reconstruction time. S-CG-2-NA has superior spatial resolution to all algorithms while still maintaining good noise reduction and is uniquely stable from over iterating. Conclusions. Both optimal algorithms (FISTA-TV and S-CG-2-NA) are stable from over iterating and have excellent edge detection with ESF MTF 50% values of 1.266 mm−1 and 0.992 mm−1. FISTA-TV had the greatest noise reduction with SNR, CNR and SNU values of 424, 434 and 0.91 × 10−4, respectively. However, low spatial resolution makes FISTA-TV only viable for large field dosimetry. S-CG-2-NA has better spatial resolution than FISTA-TV with PSF and LSF MTF 50% values of 1.581 mm−1 and 0.738 mm−1, but less noise reduction. S-CG-2-NA still maintains good SNR, CNR, and SNU values of 168, 158 and 1.13 × 10−4, respectively. Thus, S-CG-2-NA is a well rounded reconstruction algorithm that would be the preferable choice for small field dosimetry.

Boosting MR Image Impulse Noise Removal With Overlapping Group Sparse Fractional-Order Total Variation and Minimax Concave Penalty

The acquisition and transmission of magnetic resonance images are susceptible to noise, particularly impulse noise. Although the method based on the ℓ0-norm and overlapping group sparse total variation (ℓ0-OGSTV) is effective for impulse noise image restoration, it can only mitigate the staircase artifacts to a certain extent. To boost the impulse noise removal performance of ℓ0-OGSTV, we propose a new restoration model that consists of two terms. Specifically, in the first term, we keep using the ℓ0-norm as the data fidelity term to eliminate impulse noise. In the second term, we first introduce an overlapping group sparsity fractional-order total variation regularizer to eliminate staircase artifacts while preserving structural information. Then, we adopt the minimax-concave penalty to further accurately estimate the image edges. Finally, we employ an alternate direction method of multipliers to solve the proposed optimization model. Clinical experiments demonstrate its effectiveness in denoising medical images.

Radiologists' Rating for Comparative Qualitative Assessment of Intravoxel Incoherent Motion Using Novel Analysis Methods.

The objective was to assess qualitative interpretability and quantitative precision and reproducibility of intravoxel incoherent motion ( IVIM) parametric images evaluated using novel IVIM analysis methods for diagnostic accuracy. Intravoxel incoherent motion datasets of 55 patients (male/female = 41:14; age = 17.8 ± 5.5 years) with histopathology-proven osteosarcoma were analyzed. Intravoxel incoherent motion parameters-diffusion coefficient ( D ), perfusion fraction ( f ), and perfusion coefficient ( D* )-were estimated using 5 IVIM analysis methods-(i) biexponential (BE) model, (ii) BE-segmented fitting 2-parameter (BESeg-2), (iii) BE-segmented fitting 1-parameter (BESeg-1), (iv) BE model with total variation penalty function (BE + TV), and (v) BE model with Huber penalty function (BE + HPF). Qualitative scoring in a 5-point Likert scale (uninterpretable: 1; poor: 2; fair: 3; good: 4; excellent: 5) was performed by 2 radiologists for 4 criteria: (a) tumor shape and margin, (b) morphologic correlation, (c) noise suppression, and (d) overall interpretability. Interobserver agreement was evaluated using Spearman rank-order correlation ( rs ). Precision and reproducibility were evaluated using within-subject coefficient of variation (wCV) and between-subject coefficient of variation (bCV). BE + TV and BE + HPF produced significantly ( P < 10 -3 ) higher qualitative scores for D (fair-good [3.3-3.8]) than BE (poor [2.3]) and for D* (poor-fair [2.2-2.7]) and f (fair-good [3.2-3.8]) than BE, BESeg-2, and BESeg-1 ( D* : uninterpretable-poor [1.3-1.9] and f : poor-fair [1.5-3]). Interobserver agreement for qualitative scoring was rs = 0.48-0.59, P < 0.009. BE + TV and BE + HPF showed significantly ( P < 0.05) improved reproducibility in estimating D (wCV: 24%-31%, bCV: 21%-31% improvement) than the BE method and D* (wCV: 4%-19%, bCV: 5%-19% improvement) and f (wCV: 25%-49%, bCV: 25%-47% improvement) than BE, BESeg-2, and BESeg-1 methods. BE + TV and BE + HPF demonstrated qualitatively and quantitatively improved IVIM parameter estimation and may be considered for clinical use further.

Fast Compressed Sensing of 3D Radial T1 Mapping with Different Sparse and Low-Rank Models.

Knowledge of the relative performance of the well-known sparse and low-rank compressed sensing models with 3D radial quantitative magnetic resonance imaging acquisitions is limited. We use 3D radial T1 relaxation time mapping data to compare the total variation, low-rank, and Huber penalty function approaches to regularization to provide insights into the relative performance of these image reconstruction models. Simulation and ex vivo specimen data were used to determine the best compressed sensing model as measured by normalized root mean squared error and structural similarity index. The large-scale compressed sensing models were solved by combining a GPU implementation of a preconditioned primal-dual proximal splitting algorithm to provide high-quality T1 maps within a feasible computation time. The model combining spatial total variation and locally low-rank regularization yielded the best performance, followed closely by the model combining spatial and contrast dimension total variation. Computation times ranged from 2 to 113 min, with the low-rank approaches taking the most time. The differences between the compressed sensing models are not necessarily large, but the overall performance is heavily dependent on the imaged object.

Magnetic Resonance Image Denoising Based on Laplacian Prior Sparsity Constraint and Nonconvex Second-Order TV Penalty

Magnetic resonance (MR) imaging is considered as a very powerful imaging modality in clinical examination, but the process of image acquisition and transmission will be affected by noise, resulting in the degradation of imaging quality. In this paper, based on the Laplacian prior sparsity constraint and the nonconvex second order total variation (TV) penalty, we propose a MR images denoising model which consists of three terms. Specifically, in the first term, we use the L2-norm as the fidelity term to control the proximity between the observed image and the recovered MR image. Then, we introduce the Laplacian sparse prior constraint as the second term to mitigate the staircase artifacts in the recovered image. In the third term, we adopt the nonconvex second-order TV penalty to preserve important textures and edges. Finally, we use the alternating direction method of multipliers to solve the corresponding minimization problem. Comparative experiments on clinical data demonstrate the effectiveness of our approach in terms of PSNR and SSIM values.

Total Variation-Based Distributed Kalman Filtering for Resiliency Against Byzantines

This article proposes a distributed Kalman filter (DKF) with enhanced robustness against Byzantine adversaries. A Byzantine agent is a legitimate network agent that, unlike an honest agent, manipulates information before sharing it with neighbors to impair the overall system performance. In contrast to the literature, the DKF is modeled as a distributed optimization problem where resiliency against Byzantine agents is accomplished by employing a total variation (TV) penalty term. We utilize a distributed subgradient algorithm to compute the state estimate and error covariance matrix updates of the DKF. Additionally, we prove that the proposed suboptimal solution converges to a neighborhood of the optimal centralized solution of the KF with a bounded radius when Byzantine agents are present. Numerical simulations corroborate the theoretical findings and demonstrate the robustness of the proposed DKF against Byzantine attacks.

The regularization paths of total variation-penalized regression splines

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 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.

Pancreatic Mass Characterization Using IVIM-DKI MRI and Machine Learning-Based Multi-Parametric Texture Analysis.

Non-invasive characterization of pancreatic masses aids in the management of pancreatic lesions. Intravoxel incoherent motion-diffusion kurtosis imaging (IVIM-DKI) and machine learning-based texture analysis was used to differentiate pancreatic masses such as pancreatic ductal adenocarcinoma (PDAC), pancreatic neuroendocrine tumor (pNET), solid pseudopapillary epithelial neoplasm (SPEN), and mass-forming chronic pancreatitis (MFCP). A total of forty-eight biopsy-proven patients with pancreatic masses were recruited and classified into pNET (n = 13), MFCP (n = 6), SPEN (n = 4), and PDAC (n = 25) groups. All patients were scanned for IVIM-DKI sequences acquired with 14 b-values (0 to 2500 s/mm2) on a 1.5T MRI. An IVIM-DKI model with a 3D total variation (TV) penalty function was implemented to estimate the precise IVIM-DKI parametric maps. Texture analysis (TA) of the apparent diffusion coefficient (ADC) and IVIM-DKI parametric map was performed and reduced using the chi-square test. These features were fed to an artificial neural network (ANN) for characterization of pancreatic mass subtypes and validated by 5-fold cross-validation. Receiver operator characteristics (ROC) analyses were used to compute the area under curve (AUC). Perfusion fraction (f) was significantly higher (p &lt; 0.05) in pNET than PDAC. The f showed better diagnostic performance for PDAC vs. MFCP with AUC:0.77. Both pseudo-diffusion coefficient (D*) and f for PDAC vs. pNET showed an AUC of 0.73. ADC and diffusion coefficient (D) showed good diagnostic performance for pNET vs. MFCP with AUC: 0.79 and 0.76, respectively. In the TA of PDAC vs. non-PDAC, f and combined IVIM-DKI parameters showed high accuracy ≥ 84.3% and AUC ≥ 0.84. Mean f and combined IVIM-DKI parameters estimated that the IVIM-DKI model with TV texture features has the potential to be helpful in characterizing pancreatic masses.

Non-invasive intravoxel incoherent motion MRI in prediction of histopathological response to neoadjuvant chemotherapy and survival outcome in osteosarcoma at the time of diagnosis

BackgroundEarly prediction of response to neoadjuvant chemotherapy (NACT) is important to aid personalized treatment in osteosarcoma. Diffusion-weighted Intravoxel Incoherent Motion (IVIM) MRI was used to evaluate the predictive value for response to NACT and survival outcome in osteosarcoma.MethodsTotal fifty-five patients with biopsy-proven osteosarcoma were recruited prospectively, among them 35 patients were further analysed. Patients underwent 3 cycles of NACT (Cisplatin + Doxorubicin) followed by surgery and response adapted adjuvant chemotherapy. Treatment outcomes were histopathological response to NACT (good-response ≥ 50% necrosis and poor-response < 50% necrosis) and survival outcome (event-free survival (EFS) and overall survival (OS)). IVIM MRI was acquired at 1.5T at baseline (t0), after 1-cycle (t1) and after 3-cycles (t2) of NACT. Quantitative IVIM parameters (D, D*, f & D*.f) were estimated using advanced state-of-the-art spatial penalty based IVIM analysis method bi-exponential model with total-variation penalty function (BETV) at 3 time-points and histogram analysis was performed.ResultsGood-responders: Poor-responders ratio was 13 (37%):22 (63%). EFS and OS were 31% and 69% with 16.27 and 25.9 months of median duration respectively. For predicting poor-response to NACT, IVIM parameters showed AUC = 0.87, Sensitivity = 86%, Specificity = 77% at t0, and AUC = 0.96, Sensitivity = 86%, Specificity = 100% at t1. Multivariate Cox regression analysis showed smaller tumour volume (HR = 1.002, p = 0.001) higher ADC-25th-percentile (HR = 0.047, p = 0.005) & D-Mean (HR = 0.1, p = 0.023) and lower D*-Mean (HR = 1.052, p = 0.039) were independent predictors of longer EFS (log-rank p-values: 0.054, 0.0034, 0.0017, 0.0019 respectively) and non-metastatic disease (HR = 4.33, p < 10–3), smaller tumour-volume (HR = 1.001, p = 0.042), lower D*-Mean (HR = 1.045, p = 0.056) and higher D*.f-skewness (HR = 0.544, p = 0.048) were independent predictors of longer OS (log-rank p-values: < 10–3, 0.07, < 10–3, 0.019 respectively).ConclusionIVIM parameters obtained with a 1.5T scanner along with novel BETV method and their histogram analysis indicating tumour heterogeneity were informative in characterizing NACT response and survival outcome in osteosarcoma.

A data analysis of natural gas prices using penalized median regression splines

We carry out a study on a natural gas prices data analysis based on a penalized median regression spline estimator with B-spline and total variation penalty. Once we express the estimator by a linear combination of a linear B-splines, the coefficients are estimated by minimizing a penalized check loss function. A coordinate descent algorithm is introduced to handle the special penalty determined by the B-spline coefficients. In implementation, we adopt the form of an univariate weighted absolute function, which is a convex and piecewise linear function, and find its slope to find the minimum of each coordinate. We also illustrate the performance of the proposed method using some numerical studies and data analysis. The performance of the proposed estimator is studied through both numerical simulations and the natural gas prices data sets.

Sequential linear integer programming for integer optimal control with total variation regularization

We propose a trust-region method that solves a sequence of linear integer programs to tackle integer optimal control problems regularized with a total variation penalty. The total variation penalty implies that the considered integer control problems admit minimizers. We introduce a local optimality concept for the problem, which arises from the infinite-dimensional perspective. In the case of a one-dimensional domain of the control function, we prove convergence of the iterates produced by our algorithm to points that satisfy first-order stationarity conditions for local optimality. We demonstrate the theoretical findings on a computational example.

1-Bit Compressed Sensing via an L1-TV Regularization Method

This paper considers the 1-bit compressed sensing (1-bit CS) of signals that are simultaneously sparse and gradient sparse. Since L1-norm and total variation (TV) penalties are beneficial for reconstructing element-sparse and gradient-sparse signals, respectively, we combine both to propose the L1-TV regularization model for 1-bit CS. We show that the proposed model has a closed-form solution so that one can easily calculate. Despite the apparent simplicity, our theoretical analysis reveals that the solution provides an approximate estimate for the underlying signal. Besides, in the case of introducing a dither vector, we develop an adaptive algorithm to accelerate the decay rate of recovery error. The key idea is that generating the dither for each iteration relying on the last estimate. In addition to theoretical analysis, we conduct a series of experiments on both synthetic and real-world data to show the superiority of our algorithms.

Image Reconstruction of Conductivity Distribution With Combined L 1-Norm Fidelity and Hybrid Total Variation Penalty

Image reconstruction of conductivity distribution is a highly nonlinear ill-posed inverse problem in electrical impedance tomography (EIT). To solve the problem, Tikhonov regularization and total variation (TV) regularization methods have been generally adopted. However, reconstructed images suffer from excessive smoothness or staircase effect. In this article, a novel approach is proposed for imaging conductivity distribution. Unlike traditional regularization methods, fidelity term based on <inline-formula> <tex-math notation="LaTeX">$L_{1}$ </tex-math></inline-formula>-norm is introduced to stabilize the ill-posed problem and enforce sparsity in the solution. Moreover, a first-order and high-order TV combined hybrid penalty term is introduced to keep the sharp profile and restrain the staircase effect. During image reconstruction, regularization parameter and weighting factor are determined by the adaptive method. In addition, a soft-thresholding operator is introduced to remove artifact and enhance robustness to noise. Numerical simulations have been performed to validate the performance of the proposed approach against Landweber, Tikhonov, TV, high-order TV, and iterated soft-thresholding methods. The impacts of conductivity distribution, conductivity contrast, contact impedance, and boundary shape on reconstruction are studied. Besides, robustness to noise and computation time are evaluated. The performance of the proposed approach is also verified by phantom experiments. Simulation and experimental results demonstrate that the proposed approach performs well in image reconstruction of conductivity distribution. Clearer background is observed and inclusions with sharp or smooth edges can be better reconstructed.

Fast non-uniform Fourier transform based regularization for sparse-view large-size CT reconstruction

&lt;p style='text-indent:20px;'&gt;Spare-view CT imaging is advantageous to decrease the radiation exposure, acquisition time and computational cost, but suffers from severe streak noise in reconstruction if the classical filter back projection method is employed. Although a few compressed sensing based algorithms have recently been proposed to remedy the insufficiency of projections and have achieved remarkable improvement in reconstruction quality, they face computational challenges for large-scale CT images (e.g., larger than 2000℅2000 pixels). In this paper, we present a fast non-uniform Fourier transform based reconstruction method, targeting at under-sampling high resolution Synchrotron-based micro-CT imaging. The proposed method manipulates the Fourier slice theorem to avoid the involvement of large-scale system matrices, and the reconstruction process is performed in the Fourier domain. With a total variation penalty term, the proposed method can be formulated into an unconstrained minimization problem, which is able to be efficiently solved by the limited-memory BFGS algorithm. Moreover, direct non-uniform Fourier transform is computationally costly, so the developed NUFFT algorithm is adopted to approximate it with little loss of quality. Numerical simulation is implemented to compare the proposed method with some other competing approaches, and then real data obtained from the Australia Synchrotron facility are tested to demonstrate the practical applications of the proposed approach. In short, the significance of the proposed approach includes (1) that it can handle high-resolution CT images with millions of pixels while several other contemporary methods fail; (2) that it can achieve much better reconstruction quality than other methods when the projections are insufficient.&lt;/p&gt;

Hyperspectral Image Restoration Using 3-D Hybrid Higher Degree Total Variation Regularized Nonconvex Local Low-Rank Tensor Recovery

The degradation of spaceborne hyperspectral images (HSIs) usually results from various types of noise. In this letter, we propose a 3D hybrid higher degree total variation regularized nonconvex local low-rank tensor recovery (H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> DTV-NLRTR) model to restore the HSIs. Inspired by the good performance of the higher degree total variation penalty in image denoising, we first develop a 3D hybrid higher degree total variation penalty term, which is able to capture the fine image details and edges along the spatial dimensions and spectral dimension. The tensor multi-Schatten- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> norm is chosen as the relaxation of the low-rank tensor constraint, which can not only separate the low-rank clean HSI patches from noisy images effectively but also improve the computational efficiency. The proposed H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> DTV-NLRTR model can simultaneously characterize the spectral correlation and the spatial structure of the HSI dataset by incorporating the H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> DTV penalty in the nonconvex local low-rank tensor recovery problem. In addition, we adopt a fast iterative majorize-minimize algorithm to efficiently solve the corresponding optimization problem. The numerical experiments on both simulated and real HSI datasets demonstrate that the proposed algorithm provides consistently improved restoration results compared with the state-of-the-art algorithms.

Block-Sparse Signal Recovery via General Total Variation Regularized Sparse Bayesian Learning

One of the main challenges in block-sparse signal recovery, as encountered in, e.g., multi-antenna mmWave channel models, is block-patterned estimation <i>without knowledge of block sizes and boundaries</i>. We propose a novel Sparse Bayesian Learning (SBL) method for block-sparse signal recovery under unknown block patterns. Contrary to conventional approaches that impose block-promoting regularization on the signal components, we apply two classes of <i>hyperparameter</i> regularizers for the SBL cost function, inspired by total variation (TV) denoising. The first class relies on a conventional TV difference unit and allows performing the SBL inference iteratively through a set of convex optimization problems, enabling a flexible choice of numerical solvers. The second class incorporates a region-aware TV penalty to penalize the signal and zero blocks in a dissimilar manner, enhancing the performance. We derive an alternating optimization algorithm based on expectation-maximization to perform the SBL inference through computationally efficient parallel updates for both the regularizer classes. The numerical results show that the proposed TV-regularized SBL algorithm is robust to the nature of the block structure and is capable of recovering signals with both block-patterned and isolated components, proving effective for various signal recovery systems.

Unsupervised deep learning with higher-order total-variation regularization for multidimensional seismic data reconstruction

In 3D marine seismic acquisition, the seismic wavefield is not sampled uniformly in the spatial directions. This leads to a seismic wavefield consisting of irregularly and sparsely populated traces with large gaps between consecutive sail lines, especially in the near offsets. The problem of reconstructing the complete seismic wavefield from a subsampled and incomplete wavefield is formulated as an underdetermined inverse problem. We have investigated unsupervised deep learning based on a convolutional neural network for multidimensional wavefield reconstruction of irregularly populated traces defined on a regular grid. Our network is based on an encoder-decoder architecture with an overcomplete latent representation, including appropriate regularization penalties to stabilize the solution. We proposed a combination of penalties, which consists of the [Formula: see text]-norm penalty on the network parameters, and a first- and second-order total-variation penalty on the model. We determined the performance of our method on broadband synthetic data and field data represented by constant-offset gathers from a source-over-cable data set from the Barents Sea. In the field data example, we compare the results to a full production flow from a contractor company, which is based on a 5D Fourier interpolation approach. In this example, our approach displays improved reconstruction of the wavefield with less noise in the sparse near offsets compared with the industry approach, which leads to improved structural definition of the near offsets in the migrated sections.