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Blind image deblurring is a challenging low-level vision task that involves estimating the unblurred image when the blur kernel is unknown. In this paper, we present a self-supervised multi-scale blind image deblurring method to jointly…

Computer Vision and Pattern Recognition · Computer Science 2024-09-04 Lening Guo , Jing Yu , Ning Zhang , Chuangbai Xiao

Regularization of ill-posed linear inverse problems via $\ell_1$ penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an $\ell_1$ penalized functional is via an…

Numerical Analysis · Mathematics 2013-01-01 I. Daubechies , M. Fornasier , I. Loris

We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to…

Systems and Control · Computer Science 2016-06-16 Reza Arablouei

This paper concerns iterative reconstruction for low-dose and few-view CT by minimizing a data-fidelity term regularized with the Total Variation (TV) penalty. We propose a very fast iterative algorithm to solve this problem. The algorithm…

Medical Physics · Physics 2017-02-01 Hiroyuki Kudo , Fukashi Yamazaki , Takuya Nemoto , Keita Takaki

We introduce a new algorithm for complex image reconstruction with separate regularization of the image magnitude and phase. This optimization problem is interesting in many different image reconstruction contexts, although is nonconvex and…

Signal Processing · Electrical Eng. & Systems 2020-12-17 Yunsong Liu , Justin P. Haldar

Total variation (TV) regularization is a classical tool for image denoising, but its convex $\ell_1$ formulation often leads to staircase artifacts and loss of contrast. To address these issues, we introduce the Transformed $\ell_1$ (TL1)…

Image and Video Processing · Electrical Eng. & Systems 2025-11-20 Nabiha Choudhury , Jianqing Jia , Yifei Lou

We tackle the problem of recovering an unknown signal observed in an ill-posed inverse problem framework. More precisely, we study a procedure commonly used in numerical analysis or image deblurring: minimizing an empirical loss function…

Statistics Theory · Mathematics 2007-09-18 J. M. Loubes

This paper proposes the Proximal Iteratively REweighted (PIRE) algorithm for solving a general problem, which involves a large body of nonconvex sparse and structured sparse related problems. Comparing with previous iterative solvers for…

Numerical Analysis · Computer Science 2014-04-29 Canyi Lu , Yunchao Wei , Zhouchen Lin , Shuicheng Yan

The problem of deblurring an image when the blur kernel is unknown remains challenging after decades of work. Recently there has been rapid progress on correcting irregular blur patterns caused by camera shake, but there is still much room…

Computer Vision and Pattern Recognition · Computer Science 2013-02-08 Paul Shearer , Anna C. Gilbert , Alfred O. Hero

We propose a globally convergent alternating minimization (AM) algorithm for image reconstruction in transmission tomography, which extends automatic relevance determination (ARD) to Poisson noise models with Beer's law. The algorithm…

The augmented Lagrangian (AL) method that solves convex optimization problems with linear constraints has drawn more attention recently in imaging applications due to its decomposable structure for composite cost functions and empirical…

Optimization and Control · Mathematics 2015-11-30 Hung Nien , Jeffrey A. Fessler

The problem of image blurring is one of the most studied topics in the field of image processing. Image blurring is caused by various factors such as hand or camera shake. To restore the blurred image, it is necessary to know information…

Computer Vision and Pattern Recognition · Computer Science 2023-10-03 M. Zarebnia , R. Parvaz

The Augmented Lagragian Method (ALM) and Alternating Direction Method of Multiplier (ADMM) have been powerful optimization methods for general convex programming subject to linear constraint. We consider the convex problem whose objective…

Optimization and Control · Mathematics 2015-11-18 Canyi Lu , Huan Li , Zhouchen Lin , Shuicheng Yan

This work proposes a general learned proximal alternating minimization algorithm, LPAM, for solving learnable two-block nonsmooth and nonconvex optimization problems. We tackle the nonsmoothness by an appropriate smoothing technique with…

Optimization and Control · Mathematics 2026-03-10 Yunmei Chen , Lezhi Liu , Lei Zhang

This paper concerns a class of composite image reconstruction models for impluse noise removal, which is rather general and covers existing convex and nonconvex models proposed for reconstructing images with impluse noise. For this…

Optimization and Control · Mathematics 2024-03-27 Bujin Li , Shaohua Pan , Tieyong Zeng

In this paper, we propose a novel solution for non-convex problems of multiple variables, especially for those typically solved by an alternating minimization (AM) strategy that splits the original optimization problem into a set of…

Machine Learning · Computer Science 2022-06-28 Jingyuan Xia , Shengxi Li , Jun-Jie Huang , Imad Jaimoukha , Deniz Gunduz

Total Variation (TV) is a popular regularization strategy that promotes piece-wise constant signals by constraining the $\ell_1$-norm of the first order derivative of the estimated signal. The resulting optimization problem is usually…

Optimization and Control · Mathematics 2020-10-20 Hamza Cherkaoui , Jeremias Sulam , Thomas Moreau

We develop two new variants of alternating direction methods of multipliers (ADMM) and two parallel primal-dual decomposition algorithms to solve a wide range class of constrained convex optimization problems. Our approach relies on a novel…

Optimization and Control · Mathematics 2018-06-15 Quoc Tran-Dinh , Yuzixuan Zhu

Non-blind image deblurring is typically formulated as a linear least-squares problem regularized by natural priors on the corresponding sharp picture's gradients, which can be solved, for example, using a half-quadratic splitting method…

Computer Vision and Pattern Recognition · Computer Science 2020-09-16 Thomas Eboli , Jian Sun , Jean Ponce

Augmented Lagrangian method (ALM) has been popularly used for solving constrained optimization problems. Practically, subproblems for updating primal variables in the framework of ALM usually can only be solved inexactly. The convergence…

Optimization and Control · Mathematics 2018-03-28 Yangyang Xu