Related papers: Regularizing Ill-Posed Inverse Problems: Deblurrin…

Sliced Inverse Regression (SIR) is an effective method for dimension reduction in high-dimensional regression problems. The original method, however, requires the inversion of the predictors covariance matrix. In case of collinearity…

Inverse problems in image processing are typically cast as optimization tasks, consisting of data-fidelity and stabilizing regularization terms. A recent regularization strategy of great interest utilizes the power of denoising engines. Two…

In the present paper we consider application of overcomplete dictionaries to solution of general ill-posed linear inverse problems. In the context of regression problems, there has been enormous amount of effort to recover an unknown…

We derive and analyse a new variant of the iteratively regularized Landweber iteration, for solving linear and nonlinear ill-posed inverse problems. The method takes into account training data, which are used to estimate the interior of a…

Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, which are a necessity due to the ill-posedness of inverse problems. Tikhonov-type regularization methods are very popular in…

We study a new family of inverse problems for recovering representations of corrupted data. We assume access to a pre-trained representation learning network R(x) that operates on clean images, like CLIP. The problem is to recover the…

In this paper, the concept of matrix splitting is introduced to solve a large sparse ill-posed linear system via Tikhonov's regularization. In the regularization process, we convert the ill-posed system to a well-posed system. The…

Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional…

In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction operators. We give an extended definition of regularization…

This paper comprehensively reviews the recent development of image deblurring, including non-blind/blind, spatially invariant/variant deblurring techniques. Indeed, these techniques share the same objective of inferring a latent sharp image…

Separable nonlinear least squares problems appear in many inverse problems, including semi-blind image deblurring. The variable projection (VarPro) method provides an efficient approach for solving such problems by eliminating linear…

The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is…

In this paper, we establish universal approximation theorems for neural networks applied to general nonlinear ill-posed operator equations. In addition to the approximation error, the measurement error is also taken into account in our…

We propose a simple algorithm to locate the "corner" of an L-curve, a function often used to select the regularisation parameter for the solution of ill-posed inverse problems. The algorithm involves the Menger curvature of a circumcircle…

In this article, we dwell into the class of so-called ill-posed Linear Inverse Problems (LIP) which simply refers to the task of recovering the entire signal from its relatively few random linear measurements. Such problems arise in a…

Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…

Image deblurring remains a central research area within image processing, critical for its role in enhancing image quality and facilitating clearer visual representations across diverse applications. This paper tackles the optimization…

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…

In this work we present a novel optimization strategy for image reconstruction tasks under analysis-based image regularization, which promotes sparse and/or low-rank solutions in some learned transform domain. We parameterize such…

This is a review on blind image deblurring. First, we formulate the blind image deblurring problem and explain why it is challenging. Next, we bring some psychological and cognitive studies on the way our human vision system deblurs. Then,…