Related papers: Support Recovery for Sparse Deconvolution of Posit…
We consider the problem of recovering an unknown effectively $(s_1,s_2)$-sparse low-rank-$R$ matrix $X$ with possibly non-orthogonal rank-$1$ decomposition from incomplete and inaccurate linear measurements of the form $y = \mathcal A (X) +…
We study the information-theoretic limits of exactly recovering the support of a sparse signal using noisy projections defined by various classes of measurement matrices. Our analysis is high-dimensional in nature, in which the number of…
We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transform. Our key…
The task of finding a sparse signal decomposition in an overcomplete dictionary is made more complicated when the signal undergoes an unknown modulation (or convolution in the complementary Fourier domain). Such simultaneous sparse recovery…
In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
Short-and-sparse deconvolution (SaSD) aims to recover a short kernel and a long and sparse signal from their convolution. In the literature, formulations of blind deconvolution is either a convex programming via a matrix lifting of…
We investigate the reconstruction of multivariate functions from samples using sparse recovery techniques. For Square Root Lasso, Orthogonal Matching Pursuit, and Compressive Sampling Matching Pursuit, we demonstrate both theoretically and…
Low-rank matrix recovery from structured measurements has been a topic of intense study in the last decade and many important problems like matrix completion and blind deconvolution have been formulated in this framework. An important…
This paper investigates the statistical estimation of a discrete mixing measure $\mu$0 involved in a kernel mixture model. Using some recent advances in l1-regularization over the space of measures, we introduce a "data fitting and…
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…
Blind deconvolution is a ubiquitous problem of recovering two unknown signals from their convolution. Unfortunately, this is an ill-posed problem in general. This paper focuses on the {\em short and sparse} blind deconvolution problem,…
This paper concerns solving the sparse deconvolution and demixing problem using $\ell_{1,2}$-minimization. We show that under a certain structured random model, robust and stable recovery is possible. The results extend results of Ling and…
This paper advances the general theory of continuous sparse regularisation on measures with the Beurling-LASSO (BLASSO). This TV-regularised convex program on the space of measures allows to recover a sparse measure using a noisy…
In this paper, we recover sparse signals from their noisy linear measurements by solving nonlinear differential inclusions, which is based on the notion of inverse scale space (ISS) developed in applied mathematics. Our goal here is to…
This paper presents a sharp geometric analysis of the recovery performance of sparse regularization. More specifically, we analyze the BLASSO method which estimates a sparse measure (sum of Dirac masses) from randomized sub-sampled…
This note presents a unified analysis of the recovery of simple objects from random linear measurements. When the linear functionals are Gaussian, we show that an s-sparse vector in R^n can be efficiently recovered from 2s log n…
We consider the problem of recovering two unknown vectors, $\boldsymbol{w}$ and $\boldsymbol{x}$, of length $L$ from their circular convolution. We make the structural assumption that the two vectors are members of known subspaces, one with…
Spike deconvolution is the problem of recovering the point sources from their convolution with a known point spread function, which plays a fundamental role in many sensing and imaging applications. In this paper, we investigate the local…
Demixing refers to the challenge of identifying two structured signals given only the sum of the two signals and prior information about their structures. Examples include the problem of separating a signal that is sparse with respect to…