Related papers: $L^0$-regularized Variational Methods for Sparse P…

This paper deals with sparse phase retrieval, i.e., the problem of estimating a vector from quadratic measurements under the assumption that few components are nonzero. In particular, we consider the problem of finding the sparsest vector…

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…

We demonstrate a simple greedy algorithm that can reliably recover a d-dimensional vector v from incomplete and inaccurate measurements x. Here our measurement matrix is an N by d matrix with N much smaller than d. Our algorithm,…

This work addresses the recovery and demixing problem of signals that are sparse in some general dictionary. Involved applications include source separation, image inpainting, super-resolution, and restoration of signals corrupted by…

Spike and slab priors play a key role in inducing sparsity for sparse signal recovery. The use of such priors results in hard non-convex and mixed integer programming problems. Most of the existing algorithms to solve the optimization…

In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts to recover the phase information of a signal from the…

Signal reconstruction in compressive sensing involves finding a sparse solution that satisfies a set of linear constraints. Several approaches to this problem have been considered in existing reconstruction algorithms. They each provide a…

In this paper, we study the ratio of the $L_1 $ and $L_2 $ norms, denoted as $L_1/L_2$, to promote sparsity. Due to the non-convexity and non-linearity, there has been little attention to this scale-invariant model. Compared to popular…

Suppose we wish to recover an n-dimensional real-valued vector x_0 (e.g. a digital signal or image) from incomplete and contaminated observations y = A x_0 + e; A is a n by m matrix with far fewer rows than columns (n << m) and e is an…

We propose a robust and efficient approach to the problem of compressive phase retrieval in which the goal is to reconstruct a sparse vector from the magnitude of a number of its linear measurements. The proposed framework relies on…

Signal recovery from nonlinear measurements involves solving an iterative optimization problem. In this paper, we present a framework to optimize the sensing parameters to improve the quality of the signal recovered by the given iterative…

We propose a method to reconstruct sparse signals degraded by a nonlinear distortion and acquired at a limited sampling rate. Our method formulates the reconstruction problem as a nonconvex minimization of the sum of a data fitting term and…

We present a strategy for the recovery of a sparse solution of a common problem in acoustic engineering, which is the reconstruction of sound source levels and locations applying microphone array measurements. The considered task bears…

We formulate a unified framework for the separation of signals that are sparse in "morphologically" different redundant dictionaries. This formulation incorporates the so-called "analysis" and "synthesis" approaches as special cases and…

The classical sparse parameter identification methods are usually based on the iterative basis selection such as greedy algorithms, or the numerical optimization of regularized cost functions such as LASSO and Bayesian posterior probability…

In this paper, a sparse-based method for the estimation of the parameters of multidimensional ($R$-D) modal (harmonic or damped) complex signals in noise is presented. The problem is formulated as $R$ simultaneous sparse approximations of…

Phase retrieval consists in the recovery of an unknown signal from phaseless measurements of its usually complex-valued Fourier transform. Without further assumptions, this problem is notorious to be severe ill posed such that the recovery…

This article considers recovery of signals that are sparse or approximately sparse in terms of a (possibly) highly overcomplete and coherent tight frame from undersampled data corrupted with additive noise. We show that the properly…

The phase retrieval problem asks to recover a natural signal $y_0 \in \mathbb{R}^n$ from $m$ quadratic observations, where $m$ is to be minimized. As is common in many imaging problems, natural signals are considered sparse with respect to…

Noiseless compressive sensing is a protocol that enables undersampling and later recovery of a signal without loss of information. This compression is possible because the signal is usually sufficiently sparse in a given basis. Currently,…