Related papers: Sparse l1 Regularisation of Matrix Valued Models f…

Sparse coding refers to the pursuit of the sparsest representation of a signal in a typically overcomplete dictionary. From a Bayesian perspective, sparse coding provides a Maximum a Posteriori (MAP) estimate of the unknown vector under a…

Conventional sparse phase retrieval schemes can recover sparse signals from the magnitude of linear measurements only up to a global phase ambiguity. This work proposes a novel approach that instead utilizes the magnitude of affine…

We consider the problem of recovering signals from their power spectral density. This is a classical problem referred to in literature as the phase retrieval problem, and is of paramount importance in many fields of applied sciences. In…

We study the problem of recovering sparse signals from compressed linear measurements. This problem, often referred to as sparse recovery or sparse reconstruction, has generated a great deal of interest in recent years. To recover the…

This article explores a variant of Kac's famous problem, "Can one hear the shape of a drum?", by addressing a geometric inverse problem in acoustics. Our objective is to reconstruct the shape of a cuboid room using acoustic signals measured…

In this paper, we propose a sparsity-promoting feedback control design for stochastic linear systems with multiplicative noise. The objective is to identify a sparse control architecture that optimizes the closed-loop performance while…

This note considers the unstructured sparse recovery problems in a general form. Examples include rational approximation, spectral function estimation, Fourier inversion, Laplace inversion, and sparse deconvolution. The main challenges are…

Sparse and convolutional constraints form a natural prior for many optimization problems that arise from physical processes. Detecting motifs in speech and musical passages, super-resolving images, compressing videos, and reconstructing…

We propose and analyze an online algorithm for reconstructing a sequence of signals from a limited number of linear measurements. The signals are assumed sparse, with unknown support, and evolve over time according to a generic nonlinear…

In this letter, we propose an algorithm for recovery of sparse and low rank components of matrices using an iterative method with adaptive thresholding. In each iteration, the low rank and sparse components are obtained using a thresholding…

Compressed sensing has a wide range of applications that include error correction, imaging, radar and many more. Given a sparse signal in a high dimensional space, one wishes to reconstruct that signal accurately and efficiently from a…

We propose a new framework -- Square Root Principal Component Pursuit -- for low-rank matrix recovery from observations corrupted with noise and outliers. Inspired by the square root Lasso, this new formulation does not require prior…

We consider the problem of estimating a rank-one matrix in Gaussian noise under a probabilistic model for the left and right factors of the matrix. The probabilistic model can impose constraints on the factors including sparsity and…

Given a known matrix that is the sum of a low rank matrix and a masked sparse matrix, we wish to recover both the low rank component and the sparse component. The sparse matrix is masked in the sense that a linear transformation has been…

In traditional compressed sensing theory, the dictionary matrix is given a priori, whereas in real applications this matrix suffers from random noise and fluctuations. In this paper we consider a signal model where each column in the…

We consider the problem of sparse signal recovery from noisy measurements. Many of frequently used recovery methods rely on some sort of tuning depending on either noise or signal parameters. If no estimates for either of them are…

In this paper, we consider the problem of recovering a sparse signal from noisy linear measurements using the so called LASSO formulation. We assume a correlated Gaussian design matrix with additive Gaussian noise. We precisely analyze the…

A robust algorithm is proposed to reconstruct the spatial support and the Lam\'e parameters of multiple inclusions in a homogeneous background elastic material using a few measurements of the displacement field over a finite collection of…

Many popular statistical models, such as factor and random effects models, give arise a certain type of covariance structures that is a summation of low rank and sparse matrices. This paper introduces a penalized approximation framework to…

The role of sparse representations in the context of structured noise filtering is discussed. A strategy, especially conceived so as to address problems of an ill posed nature, is presented. The proposed approach revises and extends the…