Related papers: Beyond Moore-Penrose Part II: The Sparse Pseudoinv…
In this paper, we study the sparse nonnegative tensor factorization and completion problem from partial and noisy observations for third-order tensors. Because of sparsity and nonnegativity, the underlying tensor is decomposed into the…
Compressed sensing is a new scheme which shows the ability to recover sparse signal from fewer measurements, using $l_1$ minimization. Recently, Chartrand and Staneva shown in \cite{CS1} that the $l_p$ minimization with $0<p<1$ recovers…
Consider the generalized linear least squares (GLS) problem $\min\|Lx\|_2 \ \mathrm{s.t.} \ \|M(Ax-b)\|_2=\min$. The weighted pseudoinverse $A_{ML}^{\dag}$ is the matrix that maps $b$ to the minimum 2-norm solution of this GLS problem. By…
This paper examines fundamental error characteristics for a general class of matrix completion problems, where the matrix of interest is a product of two a priori unknown matrices, one of which is sparse, and the observations are noisy. Our…
A polynomial matrix inequality is a formula asserting that a polynomial matrix is positive semidefinite. Polynomial matrix optimization concerns minimizing the smallest eigenvalue of a symmetric polynomial matrix subject to a tuple of…
This paper presents a method for finding a sparse representation of Barron functions. Specifically, given an $L^2$ function $f$, the inverse scale space flow is used to find a sparse measure $\mu$ minimising the $L^2$ loss between the…
We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation $\mathfrak{X}$ of the sum of an approximately) low…
This paper investigates the comparative performance of two fundamental approaches to solving linear regression problems: the closed-form Moore-Penrose pseudoinverse and the iterative gradient descent method. Linear regression is a…
We consider the inverse problem of finding a magnitude-symmetric matrix (matrix with opposing off-diagonal entries equal in magnitude) with a prescribed set of principal minors. This problem is closely related to the theory of recognizing…
In this paper, a method via sparse-sparse iteration for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix is proposed. The resulting factorized sparse approximate inverse is used as a…
In this article we provide a fast computational method in order to calculate the Moore-Penrose inverse of singular square matrices and of rectangular matrices. The proposed method proves to be much faster and has significantly better…
Sparsity plays a central role in recent developments in signal processing, linear algebra, statistics, optimization, and other fields. In these developments, sparsity is promoted through the addition of an $L^1$ norm (or related quantity)…
We propose a unified framework to solve general low-rank plus sparse matrix recovery problems based on matrix factorization, which covers a broad family of objective functions satisfying the restricted strong convexity and smoothness…
Sparse representations have emerged as a powerful tool in signal and information processing, culminated by the success of new acquisition and processing techniques such as Compressed Sensing (CS). Fusion frames are very rich new signal…
This paper develops several average-case reduction techniques to show new hardness results for three central high-dimensional statistics problems, implying a statistical-computational gap induced by robustness, a detection-recovery gap and…
We consider linear inverse problems where the solution is assumed to have a sparse expansion on an arbitrary pre-assigned orthonormal basis. We prove that replacing the usual quadratic regularizing penalties by weighted l^p-penalties on the…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
We study an ill-posed linear inverse problem, where a binary sequence will be reproduced using a sparce matrix. According to the previous study, this model can theoretically provide an optimal compression scheme for an arbitrary distortion…
Finding the sparse representation of a signal in an overcomplete dictionary has attracted a lot of attention over the past years. This paper studies ProSparse, a new polynomial complexity algorithm that solves the sparse representation…
The aim of this work is to characterize linear maps of inner pro\-duct infinite-dimensional vector spaces where the Moore-Penrose inverse exists. This MP inverse generalizes the well-known Moore-Penrose inverse of a matrix $A\in…