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Motivated by the well-known Papoulis-Gerchberg algorithm, an iterative thresholding algorithm for recovery of sparse signals from few observations is proposed. The sequence of iterates turns out to be similar to that of the thresholded…

Chance-constrained programming (CCP) is one of the most difficult classes of optimization problems that has attracted the attention of researchers since the 1950s. In this survey, we focus on cases when only a limited information on the…

We present a novel stagewise strategy for improving greedy algorithms for sparse recovery. We demonstrate its efficiency both for synthesis and analysis sparse priors, where in both cases we demonstrate its computational efficiency and…

Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…

In sparse recovery, the unique sparsest solution to an under-determined system of linear equations is of main interest. This scheme is commonly proposed to be applied to signal acquisition. In most cases, the signals are not sparse…

Intensively growing approach in signal processing and acquisition, the Compressive Sensing approach, allows sparse signals to be recovered from small number of randomly acquired signal coefficients. This paper analyses some of the commonly…

Sparse signal recovery from a small number of random measurements is a well known NP-hard to solve combinatorial optimization problem, with important applications in signal and image processing. The standard approach to the sparse signal…

Spectrum sensing is an important process in cognitive radio. A number of sensing techniques that have been proposed suffer from high processing time, hardware cost and computational complexity. To address these problems, compressive sensing…

Estimating a sparse covariance matrix is a fundamental problem in high-dimensional statistics. However, thresholding methods developed for independent data are generally not directly applicable to high-dimensional time series, where…

Classical results in sparse recovery guarantee the exact reconstruction of $s$-sparse signals under assumptions on the dictionary that are either too strong or NP-hard to check. Moreover, such results may be pessimistic in practice since…

In the past decade, sparse and low-rank recovery have drawn much attention in many areas such as signal/image processing, statistics, bioinformatics and machine learning. To achieve sparsity and/or low-rankness inducing, the $\ell_1$ norm…

The recovery of sparse data is at the core of many applications in machine learning and signal processing. While such problems can be tackled using $\ell_1$-regularization as in the LASSO estimator and in the Basis Pursuit approach,…

Sparse recovery is widely applied in many fields, since many signals or vectors can be sparsely represented under some frames or dictionaries. Most of fast algorithms at present are based on solving $l^0$ or $l^1$ minimization problems and…

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…

We prove an L2 recovery bound for a family of sparse estimators defined as minimizers of some empirical loss functions -- which include hinge loss and logistic loss. More precisely, we achieve an upper-bound for coefficients estimation…

We investigate the sparse recovery problem of reconstructing a high-dimensional non-negative sparse vector from lower dimensional linear measurements. While much work has focused on dense measurement matrices, sparse measurement schemes are…

This paper investigates sparse high-dimensional linear regression, particularly examining the properties of the posterior under conditions of random design and unknown error variance. We provide consistency results for the posterior and…

The hitting set problem is a well-known NP-hard optimization problem in which, given a set of elements and a collection of subsets, the goal is to find the smallest selection of elements, such that each subset contains at least one element…

We derived the first sparse recovery guarantees for weighted $\ell_1$ minimization with sparse random matrices and the class of weighted sparse signals, using a weighted versions of the null space property to derive these guarantees. These…

In the context of sparse recovery, it is known that most of existing regularizers such as $\ell_1$ suffer from some bias incurred by some leading entries (in magnitude) of the associated vector. To neutralize this bias, we propose a class…