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Image restoration is the task of recovering a clean image from a degraded version. In most cases, the degradation is spatially varying, and it requires the restoration network to both localize and restore the affected regions. In this…

Image and Video Processing · Electrical Eng. & Systems 2022-01-04 Maitreya Suin , Kuldeep Purohit , A. N. Rajagopalan

The problem of object restoration in the case of spatially incoherent illumination is considered. A regularized solution to the inverse problem is obtained through a probabilistic approach, and a numerical algorithm based on the statistical…

Optics · Physics 2009-11-13 Enrico De Micheli , Giovanni Alberto Viano

Non-uniqueness and instability are characteristic features of image reconstruction processes. As a result, it is necessary to develop regularization methods that can be used to compute reliable approximate solutions. A regularization method…

Numerical Analysis · Mathematics 2022-12-16 Andrea Ebner , Markus Haltmeier

Most existing non-blind restoration methods are based on the assumption that a precise degradation model is known. As the degradation process can only be partially known or inaccurately modeled, images may not be well restored. Rain streak…

Computer Vision and Pattern Recognition · Computer Science 2019-07-11 Dongwei Ren , Wangmeng Zuo , David Zhang , Lei Zhang , Ming-Hsuan Yang

We present a new inner-outer iterative algorithm for edge enhancement in imaging problems. At each outer iteration, we formulate a Tikhonov-regularized problem where the penalization is expressed in the 2-norm and involves a regularization…

Numerical Analysis · Mathematics 2020-12-30 Silvia Gazzola , Misha E. Kilmer , James G. Nagy , Oguz Semerici , Eric L. Miller

Plug-and-Play (PnP) algorithms are a class of iterative algorithms that address image inverse problems by combining a physical model and a deep neural network for regularization. Even if they produce impressive image restoration results,…

Image and Video Processing · Electrical Eng. & Systems 2025-06-12 Marien Renaud , Jean Prost , Arthur Leclaire , Nicolas Papadakis

It's well-known that inverse problems are ill-posed and to solve them meaningfully one has to employ regularization methods. Traditionally, popular regularization methods have been the penalized Variational approaches. In recent years, the…

Machine Learning · Computer Science 2022-02-17 Abinash Nayak

We investigate modified steepest descent methods coupled with a loping Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization…

Numerical Analysis · Mathematics 2008-08-03 A. De Cezaro , M. Haltmeier , A. Leitao , O. Scherzer

We present a novel iterative scheme for restoring uneven illumination in grayscale images. Our approach solves, at each global iteration, a nonlinear elliptic equation for an auxiliary field $u$ and then updates the illumination via an…

Analysis of PDEs · Mathematics 2025-06-17 Dragos-Patru Covei

In this paper we address the numerical solution of nonlinear ill-posed systems by iterative regularization methods in the classes of Levenberg-Marquardt, trust-region and adaptive quadratic regularization procedures. Both with exact and…

Numerical Analysis · Mathematics 2015-04-17 Stefania Bellavia , Benedetta Morini

We aim at the solution of inverse problems in imaging, by combining a penalized sparse representation of image patches with an unconstrained smooth one. This allows for a straightforward interpretation of the reconstruction. We formulate…

Image and Video Processing · Electrical Eng. & Systems 2025-03-18 Stanislas Ducotterd , Sebastian Neumayer , Michael Unser

Image restoration aims to recover high quality images from inputs degraded by various factors, such as adverse weather, blur, or low light. While recent studies have shown remarkable progress across individual or unified restoration tasks,…

Computer Vision and Pattern Recognition · Computer Science 2026-03-30 I-Hsiang Chen , Isma Hadji , Enrique Sanchez , Adrian Bulat , Sy-Yen Kuo , Radu Timofte , Georgios Tzimiropoulos , Brais Martinez

Some iterative techniques are defined to solve reversible inverse problems and a common formulation is explained. Numerical improvements are suggested and tests validate the methods.

Optimization and Control · Mathematics 2011-12-06 Sébastien Marinesque

In this paper we present a generalized Deep Learning-based approach for solving ill-posed large-scale inverse problems occuring in medical image reconstruction. Recently, Deep Learning methods using iterative neural networks and cascaded…

Image and Video Processing · Electrical Eng. & Systems 2020-08-26 Andreas Kofler , Markus Haltmeier , Tobias Schaeffter , Marc Kachelrieß , Marc Dewey , Christian Wald , Christoph Kolbitsch

Inverse problems appear in many applications, such as image deblurring and inpainting. The common approach to address them is to design a specific algorithm for each problem. The Plug-and-Play (P&P) framework, which has been recently…

Computer Vision and Pattern Recognition · Computer Science 2018-10-12 Tom Tirer , Raja Giryes

Digital images are commonly represented as regular 2D arrays, so pixels are organized in form of a matrix addressed by integers. However, there are many image processing operations, such as rotation or motion compensation, that produce…

Computer Vision and Pattern Recognition · Computer Science 2022-05-24 Ján Koloda , Jürgen Seiler , André Kaup

State-of-the-art algorithms for imaging inverse problems (namely deblurring and reconstruction) are typically iterative, involving a denoising operation as one of its steps. Using a state-of-the-art denoising method in this context is not…

Computer Vision and Pattern Recognition · Computer Science 2016-08-03 Afonso M. Teodoro , José M. Bioucas-Dias , Mário A. T. Figueiredo

We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations…

Optimization and Control · Mathematics 2012-10-10 Manya V. Afonso , José M. Bioucas-Dias , Mário A. T. Figueiredo

Applying standard algorithms to sparse data problems in photoacoustic tomography (PAT) yields low-quality images containing severe under-sampling artifacts. To some extent, these artifacts can be reduced by iterative image reconstruction…

Numerical Analysis · Mathematics 2024-12-20 Stephan Antholzer , Johannes Schwab , Robert Nuster , Markus Haltmeier

We propose a new fast algorithm for solving one of the standard formulations of image restoration and reconstruction which consists of an unconstrained optimization problem where the objective includes an $\ell_2$ data-fidelity term and a…

Optimization and Control · Mathematics 2015-05-14 Manya V. Afonso , José M. Bioucas-Dias , Mário A. T. Figueiredo