Image restoration is one of the classical inverse problems in image processing and computer vision, which consists in recovering information about the original image from incomplete or degraded data. This paper presents analytical solution for onedimensional case of the Tikhonov regularization method and algorithm of parameter α selection by discrepancy, which finds the mostly smoothed function...

The present paper is concerned with developing tensor iterative Krylov subspace methods to solve large multi-linear equations. We use the T-product for two tensors define tubal global Arnoldi and Golub-Kahan bidiagonalization algorithms. Furthermore, we illustrate how tensor-based approaches can be exploited ill-posed problems arising from recovering blurry multichannel (color) images videos, u...

Lanczos-hybrid regularization methods have been proposed as effective approaches for solving largescale ill-posed inverse problems. Lanczos methods restrict the solution to lie in a Krylov subspace, but they are hindered by semi-convergence behavior, in that the quality of the solution first increases and then decreases. Hybrid methods apply a standard regularization technique, such as Tikhonov...

Exact-sparsity inducing prior distributions in high-dimensional Bayesian analysis typically lead to posterior distributions that are very challenging to handle by standard Markov Chain Monte Carlo methods. We propose a methodology to derive a smooth approximation of such posterior distributions. The approximation is obtained from the forward-backward approximation of the Moreau-Yosida regulariz...

In the literature on regularization, many different parameter choice methods have been proposed in both deterministic and stochastic settings. However, based on the available information, it is not always easy to know how well a particular method will perform in a given situation and how it compares to other methods. This paper reviews most of the existing parameter choice methods, and evaluate...

The problem of motion estimation, in general, is made difficult by large illumination variations and by motion discontinuities. In recent papers, we and others have proposed global approaches to deal with both problems simultaneously within the regularization framework. A major drawback of such global methods is that several regularization parameters responsible for the integration of the illum...

Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work, we propose a new regularization approach and a new regularization parameter selection approach for linear leastsquares discrete ill-posed problems. The propo...