Related papers: Iterative optimal solutions of linear matrix equat…
This paper investigates the distributed computation of the well-known linear matrix equation in the form of $AXB = F$, with the matrices A, B, X, and F of appropriate dimensions, over multi-agent networks from an optimization perspective.…
In a plethora of applications dealing with inverse problems, e.g. in image processing, social networks, compressive sensing, biological data processing etc., the signal of interest is known to be structured in several ways at the same time.…
In our paper, we consider the following general problems: check feasibility, count the number of feasible solutions, find an optimal solution, and count the number of optimal solutions in $P \cap Z^n$, assuming that $P$ is a polyhedron,…
We consider the problem of reconstructing an infinite set of sparse, finite-dimensional vectors, that share a common sparsity pattern, from incomplete measurements. This is in contrast to the work [17], where the single vector signal can be…
Hyperspectral image (HSI) super-resolution is commonly used to overcome the hardware limitations of existing hyperspectral imaging systems on spatial resolution. It fuses a low-resolution (LR) HSI and a high-resolution (HR) conventional…
In high-dimensional linear regression, the goal pursued here is to estimate an unknown regression function using linear combinations of a suitable set of covariates. One of the key assumptions for the success of any statistical procedure in…
In this article a unified approach to iterative soft-thresholding algorithms for the solution of linear operator equations in infinite dimensional Hilbert spaces is presented. We formulate the algorithm in the framework of generalized…
We investigate how to solve smooth matrix optimization problems with general linear inequality constraints on the eigenvalues of a symmetric matrix. We present solution methods to obtain exact global minima for linear objective functions,…
Solving sparse linear systems from discretized PDEs is challenging. Direct solvers have in many cases quadratic complexity (depending on geometry), while iterative solvers require problem dependent preconditioners to be robust and…
We conducted an extensive computational experiment, lasting multiple CPU-years, to optimally select parameters for two important classes of algorithms for finding sparse solutions of underdetermined systems of linear equations. We make the…
The question of fast convergence in the classical problem of high dimensional linear regression has been extensively studied. Arguably, one of the fastest procedures in practice is Iterative Hard Thresholding (IHT). Still, IHT relies…
Iterative methods based on tensors have emerged as powerful tools for solving tensor equations, and have significantly advanced across multiple disciplines. In this study, we propose two-step tensor-based iterative methods to solve the…
This paper proposes a robust fast multi-band image fusion method to merge a high-spatial low-spectral resolution image and a low-spatial high-spectral resolution image. Following the method recently developed in [1], the generalized…
In this paper, we propose a novel method for image fusion with a high-resolution panchromatic image and a low-resolution multispectral image at the same geographical location. The fusion is formulated as a convex optimization problem which…
In this work, we investigate the interval generalized Sylvester matrix equation ${\bf{A}}X{\bf{B}}+{\bf{C}}X{\bf{D}}={\bf{F}}$ and develop some techniques for obtaining outer estimations for the so-called united solution set of this…
In this paper, we consider a well-known sparse optimization problem that aims to find a sparse solution of a possibly noisy underdetermined system of linear equations. Mathematically, it can be modeled in a unified manner by minimizing…
Scalable algorithms to solve optimization and regression tasks even approximately, are needed to work with large datasets. In this paper we study efficient techniques from matrix sketching to solve a variety of convex constrained regression…
In this paper, an iterative algorithm is presented for solving Sylvester tensor equation $\mathscr{A}*_M\mathscr{X}+\mathscr{X}*_N\mathscr{C}=\mathscr{D}$, where $\mathscr{A}$, $\mathscr{C}$ and $\mathscr{D}$ are given tensors with…
An iterative method is derived for image reconstruction. Among other attributes, this method allows constraints unrelated to the radiation measurements to be incorporated into the reconstructed image. A comparison is made with the widely…
Hyperspectral remote sensing images (HSIs) are characterized by having a low spatial resolution and a high spectral resolution, whereas multispectral images (MSIs) are characterized by low spectral and high spatial resolutions. These…