Signal Processing, ISSN 0165-1684, 02/2018, Volume 143, pp. 69 - 85

•We propose a nonconvex and nonsmooth TGV model for image restoration.•We introduce two iteratively reweighted algorithms to solve the proposed model.•We...

Primal-dual algorithm | Total generalized variation (TGV) | Image restoration | Iteratively reweighed algorithm | Nonconvex | SUPERRESOLUTION | TOTAL VARIATION REGULARIZATION | RECONSTRUCTION | ALGORITHMS | LEAST-SQUARES | ENGINEERING, ELECTRICAL & ELECTRONIC | SPACE | MINIMIZATION | Image processing | Analysis | Models | Algorithms

Primal-dual algorithm | Total generalized variation (TGV) | Image restoration | Iteratively reweighed algorithm | Nonconvex | SUPERRESOLUTION | TOTAL VARIATION REGULARIZATION | RECONSTRUCTION | ALGORITHMS | LEAST-SQUARES | ENGINEERING, ELECTRICAL & ELECTRONIC | SPACE | MINIMIZATION | Image processing | Analysis | Models | Algorithms

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 07/2017, Volume 72, Issue 1, pp. 172 - 197

In this paper, we introduce a class of variational models for the restoration of ultrasound images corrupted by noise. The proposed models involve the convex...

Alternating direction method of multipliers | Total generalized variation | Iteratively reweighted algorithm | Nonconvex regularization | Ultrasound image denoising | MATHEMATICS, APPLIED | MULTIPLICATIVE NOISE | RECONSTRUCTION | RESTORATION | ALGORITHMS | SPACE | RECOVERY | REGULARIZATION | TOTAL VARIATION MINIMIZATION | NOISE REMOVAL | SPECKLE | Models | Algorithms | Mathematical optimization | Analysis | Ultrasonic waves

Alternating direction method of multipliers | Total generalized variation | Iteratively reweighted algorithm | Nonconvex regularization | Ultrasound image denoising | MATHEMATICS, APPLIED | MULTIPLICATIVE NOISE | RECONSTRUCTION | RESTORATION | ALGORITHMS | SPACE | RECOVERY | REGULARIZATION | TOTAL VARIATION MINIMIZATION | NOISE REMOVAL | SPECKLE | Models | Algorithms | Mathematical optimization | Analysis | Ultrasonic waves

Journal Article

Complexity, ISSN 1076-2787, 2019, Volume 2019, pp. 1 - 16

It has been proved that total generalized variation (TGV) can better preserve edges while suppressing staircase effect. In this paper, we propose an effective...

MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES | VARIATION MODEL | DECOMPOSITION | SYSTEMS | ITERATIVE ALGORITHM | NONCONVEX | TOTAL VARIATION MINIMIZATION | NOISE REMOVAL | Noise | Computational mathematics | Image restoration | Experiments | Image quality | Wavelet | Inverse problems | Algorithms | Mathematical analysis | Signal processing | Mathematical models | Regularization | Methods

MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES | VARIATION MODEL | DECOMPOSITION | SYSTEMS | ITERATIVE ALGORITHM | NONCONVEX | TOTAL VARIATION MINIMIZATION | NOISE REMOVAL | Noise | Computational mathematics | Image restoration | Experiments | Image quality | Wavelet | Inverse problems | Algorithms | Mathematical analysis | Signal processing | Mathematical models | Regularization | Methods

Journal Article

Computational and Applied Mathematics, ISSN 0101-8205, 3/2018, Volume 37, Issue 1, pp. 277 - 296

We propose a novel image denoising model based on the total generalized variation (TGV) regularization. In the model, a spatially dependent regularization...

Computational Mathematics and Numerical Analysis | Mathematical Applications in Computer Science | Alternating minimization | 90C26 (Nonconvex programming) | Mathematics | Spatially dependent regularization parameter selection | Applications of Mathematics | Total generalized variation (TGV) | Mathematical Applications in the Physical Sciences | Image denoising | 68U10 (Image processing) | MATHEMATICS, APPLIED | MULTIPLICATIVE NOISE | RECONSTRUCTION | ALGORITHM | RESTORATION | MODEL | SPACE | REMOVAL | MINIMIZATION | LOCAL CONSTRAINTS

Computational Mathematics and Numerical Analysis | Mathematical Applications in Computer Science | Alternating minimization | 90C26 (Nonconvex programming) | Mathematics | Spatially dependent regularization parameter selection | Applications of Mathematics | Total generalized variation (TGV) | Mathematical Applications in the Physical Sciences | Image denoising | 68U10 (Image processing) | MATHEMATICS, APPLIED | MULTIPLICATIVE NOISE | RECONSTRUCTION | ALGORITHM | RESTORATION | MODEL | SPACE | REMOVAL | MINIMIZATION | LOCAL CONSTRAINTS

Journal Article

Neurocomputing, ISSN 0925-2312, 09/2019, Volume 359, pp. 15 - 31

Total variation (TV) regularization model has the excellent performance in noise-removing and edge-preserving. However, it often yields staircase artifacts in...

Image restoration | Nonconvex | Regularization | Total variational (TV) | Staircase artifacts | RECOVERY | SIGNALS | CONVERGENCE | TOTAL VARIATION MINIMIZATION | EFFICIENT | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Models | Algorithms | Image processing | Analysis

Image restoration | Nonconvex | Regularization | Total variational (TV) | Staircase artifacts | RECOVERY | SIGNALS | CONVERGENCE | TOTAL VARIATION MINIMIZATION | EFFICIENT | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Models | Algorithms | Image processing | Analysis

Journal Article

SIAM Journal on Imaging Sciences, ISSN 1936-4954, 02/2015, Volume 8, Issue 1, pp. 331 - 372

Natural image statistics indicate that we should use nonconvex norms for most regularization tasks in image processing and computer vision. Still, they are...

Computer vision | IRLS | Kurdyka-Łojasiewicz inequality | Nonconvex total generalized variation | Majorization-minimization | IRL1 | Iteratively reweighted algorithm | Nonsmooth nonconvex optimization | MATHEMATICS, APPLIED | Kurdyka-Lojasiewicz inequality | RECONSTRUCTION | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | RESTORATION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | RECOVERY | PRIMAL-DUAL ALGORITHMS | nonconvex total generalized variation | majorization-minimization | MINIMIZATION | iteratively reweighted algorithm | nonsmooth nonconvex optimization | computer vision | CONVERGENCE | Algorithms | Tasks | Mathematical analysis | Images | Mathematical models | Regularization | Optimization

Computer vision | IRLS | Kurdyka-Łojasiewicz inequality | Nonconvex total generalized variation | Majorization-minimization | IRL1 | Iteratively reweighted algorithm | Nonsmooth nonconvex optimization | MATHEMATICS, APPLIED | Kurdyka-Lojasiewicz inequality | RECONSTRUCTION | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | RESTORATION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | RECOVERY | PRIMAL-DUAL ALGORITHMS | nonconvex total generalized variation | majorization-minimization | MINIMIZATION | iteratively reweighted algorithm | nonsmooth nonconvex optimization | computer vision | CONVERGENCE | Algorithms | Tasks | Mathematical analysis | Images | Mathematical models | Regularization | Optimization

Journal Article

SIAM JOURNAL ON IMAGING SCIENCES, ISSN 1936-4954, 2019, Volume 12, Issue 2, pp. 1001 - 1037

We propose a new space-variant anisotropic regularization term for variational image restoration, based on the statistical assumption that the gradients of the...

MATHEMATICS, APPLIED | anisotropic modeling | CONVERGENT | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | image reconstruction | MODEL | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | VARIATIONAL APPROACH | space-variant regularization | multivariate generalized Gaussian distribution | OPTIMIZATION | ADMM | TOTAL VARIATION MINIMIZATION | nonconvex variational modeling | SHAPE PARAMETER

MATHEMATICS, APPLIED | anisotropic modeling | CONVERGENT | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | image reconstruction | MODEL | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | VARIATIONAL APPROACH | space-variant regularization | multivariate generalized Gaussian distribution | OPTIMIZATION | ADMM | TOTAL VARIATION MINIMIZATION | nonconvex variational modeling | SHAPE PARAMETER

Journal Article

INVERSE PROBLEMS AND IMAGING, ISSN 1930-8337, 02/2019, Volume 13, Issue 1, pp. 117 - 147

In this article, we introduce a novel variational model for the restoration of images corrupted by multiplicative Gamma noise. The model incorporates a convex...

MATHEMATICS, APPLIED | IMAGE-RESTORATION | SCALE-SPACE | VARIATIONAL MODEL | alternating direction method of multiplier | ALGORITHMS | PHYSICS, MATHEMATICAL | EXP-MODEL | spatially adaptive regularization parameter | ALTERNATING DIRECTION METHOD | nonconvex total generalized variation | MINIMIZATION | CONVERGENCE | NONSMOOTH | iteratively reweighted l algorithm | multiplicative Gamma noise | Image denoising

MATHEMATICS, APPLIED | IMAGE-RESTORATION | SCALE-SPACE | VARIATIONAL MODEL | alternating direction method of multiplier | ALGORITHMS | PHYSICS, MATHEMATICAL | EXP-MODEL | spatially adaptive regularization parameter | ALTERNATING DIRECTION METHOD | nonconvex total generalized variation | MINIMIZATION | CONVERGENCE | NONSMOOTH | iteratively reweighted l algorithm | multiplicative Gamma noise | Image denoising

Journal Article

SIAM Journal on Imaging Sciences, ISSN 1936-4954, 2013, Volume 6, Issue 3, pp. 1385 - 1415

A nonconvex variational model is introduced which contains the l(q)-"norm," q is an element of (0, 1), of the gradient of the underlying image in the...

Trust-region method | Total variation | Superlinear convergence | Generalized Newton method | Image restoration | Nonconvex programming | Nonconvex regularization | Compressed sensing | generalized Newton method | MATHEMATICS, APPLIED | compressed sensing | RECONSTRUCTION | SIGNAL RECOVERY | nonconvex programming | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | PRIMAL-DUAL METHOD | ALGORITHMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | trust-region method | image restoration | SPARSE RECOVERY | MINIMIZATION | NEWTON METHOD | superlinear convergence | total variation | nonconvex regularization

Trust-region method | Total variation | Superlinear convergence | Generalized Newton method | Image restoration | Nonconvex programming | Nonconvex regularization | Compressed sensing | generalized Newton method | MATHEMATICS, APPLIED | compressed sensing | RECONSTRUCTION | SIGNAL RECOVERY | nonconvex programming | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | PRIMAL-DUAL METHOD | ALGORITHMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | trust-region method | image restoration | SPARSE RECOVERY | MINIMIZATION | NEWTON METHOD | superlinear convergence | total variation | nonconvex regularization

Journal Article

Mathematical Methods of Operations Research, ISSN 1432-2994, 6/2013, Volume 77, Issue 3, pp. 459 - 472

We present a new way to solve generalized Nash equilibrium problems. We assume the feasible set to be compact. Furthermore all functions are assumed to be...

Nonconvex optimization | Parametrized optimization | Calculus of Variations and Optimal Control; Optimization | Electricity spot market | Operations Research/Decision Theory | Mathematics | Real algebraic geometry | Business/Management Science, general | Transmission loss | Generalized nash equilibrium | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Spot market | Studies | Operations research | Game theory | Optimization | Mathematical analysis | Inequalities | Programming | Mathematical models | Representations

Nonconvex optimization | Parametrized optimization | Calculus of Variations and Optimal Control; Optimization | Electricity spot market | Operations Research/Decision Theory | Mathematics | Real algebraic geometry | Business/Management Science, general | Transmission loss | Generalized nash equilibrium | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Spot market | Studies | Operations research | Game theory | Optimization | Mathematical analysis | Inequalities | Programming | Mathematical models | Representations

Journal Article

Journal of Mathematical Imaging and Vision, ISSN 0924-9907, 10/2017, Volume 59, Issue 2, pp. 296 - 317

In the usual non-local variational models, such as the non-local total variations, the image is regularized by minimizing an energy term that penalizes...

Non-convex minimization | Total variation | 90C26 | Image restoration | Mathematical Methods in Physics | Proximal alternating linearized minimization | Signal,Image and Speech Processing | Non-local regularization | Computer Science | Image Processing and Computer Vision | 65K10 | Applications of Mathematics | 49N45 | FIELDS | MATHEMATICS, APPLIED | TEXTURE SYNTHESIS | ALGORITHMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | FRAMEWORK | TOTAL VARIATION MINIMIZATION | SCHEMES | Image processing | Algorithms | Mathematics | Optimization and Control | Image Processing

Non-convex minimization | Total variation | 90C26 | Image restoration | Mathematical Methods in Physics | Proximal alternating linearized minimization | Signal,Image and Speech Processing | Non-local regularization | Computer Science | Image Processing and Computer Vision | 65K10 | Applications of Mathematics | 49N45 | FIELDS | MATHEMATICS, APPLIED | TEXTURE SYNTHESIS | ALGORITHMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | FRAMEWORK | TOTAL VARIATION MINIMIZATION | SCHEMES | Image processing | Algorithms | Mathematics | Optimization and Control | Image Processing

Journal Article

Inverse Problems, ISSN 0266-5611, 03/2018, Volume 34, Issue 4, p. 44003

Hyperspectral imaging is a cutting-edge type of remote sensing used for mapping vegetation properties, rock minerals and other materials. A major drawback of...

pansharpening | remote sensing | hyperspectral imaging | super-resolution | blind deconvolution | MATHEMATICS, APPLIED | RECONSTRUCTION | ALGORITHMS | PHYSICS, MATHEMATICAL | RECOVERY | NONCONVEX | REGISTRATION | ALTERNATING LINEARIZED MINIMIZATION | AIRBORNE LIDAR

pansharpening | remote sensing | hyperspectral imaging | super-resolution | blind deconvolution | MATHEMATICS, APPLIED | RECONSTRUCTION | ALGORITHMS | PHYSICS, MATHEMATICAL | RECOVERY | NONCONVEX | REGISTRATION | ALTERNATING LINEARIZED MINIMIZATION | AIRBORNE LIDAR

Journal Article

JOURNAL OF APPLIED REMOTE SENSING, ISSN 1931-3195, 01/2019, Volume 13, Issue 2

Convex total variation (TV) regularization models have been widely used in remote sensing image restoration problems; however, these models tend to produce...

ITERATION | nonconvex | generalization of soft-thresholding algorithm | second-order total variation regularization | ALGORITHM | DECOMPOSITION | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | LEAST-SQUARES | RECOVERY | ENVIRONMENTAL SCIENCES | REMOTE SENSING | OPTIMIZATION | remote sensing image | TOTAL VARIATION MINIMIZATION

ITERATION | nonconvex | generalization of soft-thresholding algorithm | second-order total variation regularization | ALGORITHM | DECOMPOSITION | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | LEAST-SQUARES | RECOVERY | ENVIRONMENTAL SCIENCES | REMOTE SENSING | OPTIMIZATION | remote sensing image | TOTAL VARIATION MINIMIZATION

Journal Article

Mathematical Methods of Operations Research, ISSN 1432-2994, 12/2007, Volume 66, Issue 3, pp. 373 - 407

The problem of optimizing a biconvex function over a given (bi)convex or compact set frequently occurs in theory as well as in industrial applications, for...

Biconvex sets | Biconvex optimization | Non-convex optimization | Biconvex functions | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Mathematics | Biconcave optimization | Business/Management Science, general | Generalized convexity | PROGRAMMING ALGORITHMS | MATHEMATICS, APPLIED | biconcave optimization | ROBUST STABILITY | DIFFERENTIABILITY | GOP | NONCONVEX NLPS | generalized convexity | biconvex functions | biconvex optimization | non-convex optimization | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | LOCATION-ALLOCATION PROBLEMS | CONVEX | BANACH-SPACES | biconvex sets | GLOBAL OPTIMIZATION | OPERATORS | Surveys | Algorithms | Studies | Operations research | Optimization

Biconvex sets | Biconvex optimization | Non-convex optimization | Biconvex functions | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Mathematics | Biconcave optimization | Business/Management Science, general | Generalized convexity | PROGRAMMING ALGORITHMS | MATHEMATICS, APPLIED | biconcave optimization | ROBUST STABILITY | DIFFERENTIABILITY | GOP | NONCONVEX NLPS | generalized convexity | biconvex functions | biconvex optimization | non-convex optimization | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | LOCATION-ALLOCATION PROBLEMS | CONVEX | BANACH-SPACES | biconvex sets | GLOBAL OPTIMIZATION | OPERATORS | Surveys | Algorithms | Studies | Operations research | Optimization

Journal Article

2016 International Conference on Computational Intelligence and Applications (ICCIA), 08/2016, pp. 21 - 25

Image denoising is a typically ill-conditioned inverse problem, which has attracted much attention in the fields of image processing and computer vision. In...

Image quality | Image edge detection | Computational modeling | total generalized variation | Image restoration | total variation | nonconvex optimization | Optimization | Image denoising | Image Denoising | Total Generalized Variation | Total Variation | Nonconvex Optimization

Image quality | Image edge detection | Computational modeling | total generalized variation | Image restoration | total variation | nonconvex optimization | Optimization | Image denoising | Image Denoising | Total Generalized Variation | Total Variation | Nonconvex Optimization

Conference Proceeding

IEEE Transactions on Information Theory, ISSN 0018-9448, 06/2013, Volume 59, Issue 6, pp. 3396 - 3433

Compressed sensing posits that, within limits, one can undersample a sparse signal and yet reconstruct it accurately. Knowing the precise limits to such...

joint sparsity | state evolution | minimax risk over nearly black objects | Noise reduction | group Lasso | Lasso | James-Stein | Minimization | Vectors | Partitioning algorithms | Approximate message passing (AMP) | minimax risk of soft thresholding | minimax shrinkage | Message passing | minimax risk of firm thresholding | Approximation algorithms | total variation minimization | monotone regression | Compressed sensing | nonconvex penalization | REGRESSION | SPARSITY | SMOOTHNESS | COMPUTER SCIENCE, INFORMATION SYSTEMS | POLYTOPES | ALGORITHMS | ENGINEERING, ELECTRICAL & ELECTRONIC | SHRINKAGE | DIMENSION | NEIGHBORLINESS | PARAMETER | Usage | Regression analysis | Analysis | Gaussian processes | Least squares

joint sparsity | state evolution | minimax risk over nearly black objects | Noise reduction | group Lasso | Lasso | James-Stein | Minimization | Vectors | Partitioning algorithms | Approximate message passing (AMP) | minimax risk of soft thresholding | minimax shrinkage | Message passing | minimax risk of firm thresholding | Approximation algorithms | total variation minimization | monotone regression | Compressed sensing | nonconvex penalization | REGRESSION | SPARSITY | SMOOTHNESS | COMPUTER SCIENCE, INFORMATION SYSTEMS | POLYTOPES | ALGORITHMS | ENGINEERING, ELECTRICAL & ELECTRONIC | SHRINKAGE | DIMENSION | NEIGHBORLINESS | PARAMETER | Usage | Regression analysis | Analysis | Gaussian processes | Least squares

Journal Article

SIAM Journal on Optimization, ISSN 1052-6234, 2016, Volume 26, Issue 2, pp. 891 - 921

We develop a new proximal-gradient method for minimizing the sum of a differentiable, possibly nonconvex, function plus a convex, possibly nondifferentiable,...

Nonsmooth optimization | Nonconvex optimization | Generalized projection | Proximal algorithms | PROJECTED GRADIENT METHODS | MATHEMATICS, APPLIED | proximal algorithms | MINIMIZATION | CONVEX | EUCLIDEAN DISTANCES | PROXIMAL POINT ALGORITHMS | SUBGRADIENT METHODS | CONVERGENCE | nonconvex optimization | nonsmooth optimization | generalized projection

Nonsmooth optimization | Nonconvex optimization | Generalized projection | Proximal algorithms | PROJECTED GRADIENT METHODS | MATHEMATICS, APPLIED | proximal algorithms | MINIMIZATION | CONVEX | EUCLIDEAN DISTANCES | PROXIMAL POINT ALGORITHMS | SUBGRADIENT METHODS | CONVERGENCE | nonconvex optimization | nonsmooth optimization | generalized projection

Journal Article

Journal of Mathematical Imaging and Vision, ISSN 0924-9907, 2/2017, Volume 57, Issue 2, pp. 202 - 224

Modeling magnitude magnetic resonance images (MRI) Rician denoising in a Bayesian or generalized Tikhonov framework using total variation (TV) leads naturally...

Mathematical Methods in Physics | Rician denoising | Signal,Image and Speech Processing | Magnetic resonance imaging | Total variation operator | Computer Science | Image Processing and Computer Vision | Applications of Mathematics | 1-Laplacian | Global minimizer | Nonsmooth nonconvex energy minimization | Diffusion tensor imaging | MATHEMATICS, APPLIED | INEQUALITIES | ALGORITHM | NOISE | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | TOTAL VARIATION FLOW | COMPUTER SCIENCE, SOFTWARE ENGINEERING | TOTAL VARIATION MINIMIZATION | Models | Algorithms

Mathematical Methods in Physics | Rician denoising | Signal,Image and Speech Processing | Magnetic resonance imaging | Total variation operator | Computer Science | Image Processing and Computer Vision | Applications of Mathematics | 1-Laplacian | Global minimizer | Nonsmooth nonconvex energy minimization | Diffusion tensor imaging | MATHEMATICS, APPLIED | INEQUALITIES | ALGORITHM | NOISE | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | TOTAL VARIATION FLOW | COMPUTER SCIENCE, SOFTWARE ENGINEERING | TOTAL VARIATION MINIMIZATION | Models | Algorithms

Journal Article

Inverse Problems, ISSN 0266-5611, 02/2015, Volume 31, Issue 2, pp. 25003 - 25031

We propose a new algorithmic approach to the non-smooth and non-convex Potts problem (also called piecewise-constant Mumford-Shah problem) for inverse imaging...

Piecewise-constant Mumford-Shah model | Radon transform | Image segmentation | Photoacoustic tomography | Potts model | Spherical Radon transform | MATHEMATICS, APPLIED | piecewise-constant Mumford-Shah model | LEVEL-SET APPROACH | INVERSION FORMULAS | NONCONVEX MINIMIZATION | TOTAL-VARIATION MINIMIZATION | GRAPH CUTS | PHYSICS, MATHEMATICAL | spherical Radon transform | COMPUTED-TOMOGRAPHY | LEAST-SQUARES ESTIMATORS | LIMITED DATA TOMOGRAPHY | ENERGY MINIMIZATION | image segmentation | MINIMAL PARTITIONS | photoacoustic tomography | Splitting | Segmentation | Radon | Blurred | Tomography | Segments | Inverse | Image reconstruction

Piecewise-constant Mumford-Shah model | Radon transform | Image segmentation | Photoacoustic tomography | Potts model | Spherical Radon transform | MATHEMATICS, APPLIED | piecewise-constant Mumford-Shah model | LEVEL-SET APPROACH | INVERSION FORMULAS | NONCONVEX MINIMIZATION | TOTAL-VARIATION MINIMIZATION | GRAPH CUTS | PHYSICS, MATHEMATICAL | spherical Radon transform | COMPUTED-TOMOGRAPHY | LEAST-SQUARES ESTIMATORS | LIMITED DATA TOMOGRAPHY | ENERGY MINIMIZATION | image segmentation | MINIMAL PARTITIONS | photoacoustic tomography | Splitting | Segmentation | Radon | Blurred | Tomography | Segments | Inverse | Image reconstruction

Journal Article

Mathematical Programming, ISSN 0025-5610, 4/2014, Volume 144, Issue 1, pp. 107 - 140

We propose to strengthen standard factorable relaxations of global optimization problems through the use of functional transformations of intermediate...

65K05 | Theoretical, Mathematical and Computational Physics | G$$ -convex functions | Mathematics | 90C26 | Generalized convexity | Mathematical Methods in Physics | Global optimization | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convexification | Numerical Analysis | Factorable programming | Combinatorics | G -convex functions | UNDERESTIMATION | MATHEMATICS, APPLIED | G-convex functions | CONCAVE FUNCTIONS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ENVELOPES | PROGRAMS | NONCONVEX | Studies | Analysis | Optimization | Mathematical programming | Computation | Mathematical analysis | Tools | Mathematical models | Transformations | Sharpness | Standards

65K05 | Theoretical, Mathematical and Computational Physics | G$$ -convex functions | Mathematics | 90C26 | Generalized convexity | Mathematical Methods in Physics | Global optimization | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convexification | Numerical Analysis | Factorable programming | Combinatorics | G -convex functions | UNDERESTIMATION | MATHEMATICS, APPLIED | G-convex functions | CONCAVE FUNCTIONS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ENVELOPES | PROGRAMS | NONCONVEX | Studies | Analysis | Optimization | Mathematical programming | Computation | Mathematical analysis | Tools | Mathematical models | Transformations | Sharpness | Standards

Journal Article