Related papers: An $\ell_p$ Variable Projection Method for Large-S…
Variational methods in imaging are nowadays developing towards a quite universal and flexible tool, allowing for highly successful approaches on tasks like denoising, deblurring, inpainting, segmentation, super-resolution, disparity, and…
In this paper, we consider a primal-dual domain decomposition method for total variation regularized problems appearing in mathematical image processing. The model problem is transformed into an equivalent constrained minimization problem…
This study presents the development of a spatially adaptive weighting strategy for Total Variation regularization, aimed at addressing under-determined linear inverse problems. The method leverages the rapid computation of an accurate…
Computing the regularized solution of Bayesian linear inverse problems as well as the corresponding regularization parameter is highly desirable in many applications. This paper proposes a novel iterative method, termed the Projected Newton…
Recovering jointly sparse signals in the multiple measurement vectors (MMV) setting is a fundamental problem in machine learning, but traditional methods often require careful parameter tuning or prior knowledge of the sparsity of the…
Total variation (TV) regularization is popular in image restoration and reconstruction due to its ability to preserve image edges. To date, most research activities on TV models concentrate on image restoration from blurry and noisy…
The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…
We introduce a relaxed-projection splitting algorithm for solving variational inequalities in Hilbert spaces for the sum of nonsmooth maximal monotone operators, where the feasible set is defined by a nonlinear and nonsmooth continuous…
Total variation regularization based on the l1 norm is ubiquitous in image reconstruction. However, the resulting reconstructions are not always as sparse in the edge domain as desired. Iteratively reweighted methods provide some…
Tikhonov regularization is a widely used technique in solving inverse problems that can enforce prior properties on the desired solution. In this paper, we propose a Krylov subspace based iterative method for solving linear inverse problems…
In the context of optical interferometry, only undersampled power spectrum and bispectrum data are accessible. It poses an ill-posed inverse problem for image recovery. Recently, a tri-linear model was proposed for monochromatic imaging,…
Optimization problems over permutation matrices appear widely in facility layout, chip design, scheduling, pattern recognition, computer vision, graph matching, etc. Since this problem is NP-hard due to the combinatorial nature of…
A novel numerical method for the estimation of large time-varying parameter (TVP) models is proposed. The updating and smoothing estimates of the TVP model are derived within the context of generalised linear least squares and through…
Non-stationary blind super-resolution is an extension of the traditional super-resolution problem, which deals with the problem of recovering fine details from coarse measurements. The non-stationary blind super-resolution problem appears…
The proliferation of saddle points, rather than poor local minima, is increasingly understood to be a primary obstacle in large-scale non-convex optimization for machine learning. Variable elimination algorithms, like Variable Projection…
We consider the discretization of a boundary value problem for a general linear second-order elliptic operator with smooth coefficients using the Virtual Element approach. As in [59] the problem is supposed to have a unique solution, but…
We consider an important class of signal processing problems where the signal of interest is known to be sparse, and can be recovered from data given auxiliary information about how the data was generated. For example, a sparse Green's…
Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…
Based on the joint bidiagonalization process of a large matrix pair $\{A,L\}$, we propose and develop an iterative regularization algorithm for the large scale linear discrete ill-posed problems in general-form regularization: $\min\|Lx\| \…
We propose an unsupervised approach for learning end-to-end reconstruction operators for ill-posed inverse problems. The proposed method combines the classical variational framework with iterative unrolling, which essentially seeks to…