Related papers: Polynomial Preconditioners for Regularized Linear …
This paper is concerned with the development, analysis and numerical realization of a novel variational model for the regularization of inverse problems in imaging. The proposed model is inspired by the architecture of generative…
The convergence rates of iterative methods for solving a linear system $\mathbf{A} x = b$ typically depend on the condition number of the matrix $\mathbf{A}$. Preconditioning is a common way of speeding up these methods by reducing that…
Machine learning techniques for the solution of inverse problems have become an attractive approach in the last decade, while their theoretical foundations are still in their infancy. In this chapter we want to pursue the study of…
In this paper, we investigate the preconditioned AOR method for solving linear systems. We study two general preconditioners and propose some lower triangular, upper triangular and combination preconditioners. For $A$ being an L-matrix, a…
When adopting a model-based formulation, solving inverse problems encountered in multiband imaging requires to define spatial and spectral regularizations. In most of the works of the literature, spectral information is extracted from the…
In the context of linear inverse problems, we propose and study a general iterative regularization method allowing to consider large classes of regularizers and data-fit terms. The algorithm we propose is based on a primal-dual diagonal…
A new polynomial preconditioner for symmetric complex linear systems based on Hermitian and skew-Hermitian splitting (HSS) for complex symmetric linear systems is herein presented. It applies to Conjugate Orthogonal Conjugate Gradient…
The standard approach for finding eigenvalues and eigenvectors of matrix polynomials starts by embedding the coefficients of the polynomial into a matrix pencil, known as linearization. Building on the pioneering work of Nakatsukasa and…
We present a two-level preconditioner for solving linear systems arising from the discretization of the elliptic, linear-elastic deformation equation, in displacement unknowns, over domains that have arbitrary geometric and topological…
Recovering high-resolution images from limited sensory data typically leads to a serious ill-posed inverse problem, demanding inversion algorithms that effectively capture the prior information. Learning a good inverse mapping from training…
First, we derive explicit computable expressions of structured backward errors of approximate eigenelements of structured matrix polynomials including symmetric, skew-symmetric, Hermitian, skew-Hermitian, even and odd polynomials. We also…
The goal of this paper is to propose preconditioners for the system of linear equations that arises from a discretization of fourth order elliptic problems using spectral element methods. These preconditioners are constructed using…
Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…
We present a novel linear solver that works well for large systems obtained from discretizing PDEs. It is robust and, for the examples we studied, the computational effort scales linearly with the number of equations. The algorithm is based…
Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
The solution of systems of linear(ized) equations lies at the heart of many problems in Scientific Computing. In particular for systems of large dimension, iterative methods are a primary approach. Stationary iterative methods are generally…
We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
Recently, with the significant developments in deep learning techniques, solving underdetermined inverse problems has become one of the major concerns in the medical imaging domain. Typical examples include undersampled magnetic resonance…
In this paper, we design constant modulus probing waveforms with good correlation properties for collocated multi-input multi-output (MIMO) radar systems. The main content is as follows: first, we formulate the design problem as a fourth…