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We study the recovery of sparse signals from underdetermined linear measurements when a potentially erroneous support estimate is available. Our results are twofold. First, we derive necessary and sufficient conditions for signal recovery…

We consider the problem of recovering a signal from nonlinear transformations, under convex constraints modeling a priori information. Standard feasibility and optimization methods are ill-suited to tackle this problem due to the…

We consider a structured estimation problem where an observed matrix is assumed to be generated as an $s$-sparse linear combination of $N$ given $n\times n$ positive-semidefinite matrices. Recovering the unknown $N$-dimensional and…

In this paper, we study a support set reconstruction problem in which the signals of interest are jointly sparse with a common support set, and sampled by joint sparsity model-2 (JSM-2) in the presence of noise. Using mathematical tools, we…

In compressed sensing, it is often desirable to consider signals possessing additional structure beyond sparsity. One such structured signal model - which forms the focus of this paper - is the local sparsity in levels class. This class has…

This paper considers the use of total variation regularization in the recovery of approximately gradient sparse signals from their noisy discrete Fourier samples in the context of compressed sensing. It has been observed over the last…

Compressed sensing is triggering a major evolution in signal acquisition. It consists in sampling a sparse signal at low rate and later using computational power for its exact reconstruction, so that only the necessary information is…

In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a…

The Compressive Sensing framework maintains relevance even when the available measurements are subject to extreme quantization, as is exemplified by the so-called one-bit compressed sensing framework which aims to recover a signal from…

Most compressed sensing algorithms do not account for the effect of saturation in noisy compressed measurements, though saturation is an important consequence of the limited dynamic range of existing sensors. The few algorithms that handle…

Recent control trends are increasingly relying on communication networks and wireless channels to close the loop for Internet-of-Things applications. Traditionally these approaches are model-based, i.e., assuming a network or channel model…

Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…

The fundamental principle underlying compressed sensing is that a signal, which is sparse under some basis representation, can be recovered from a small number of linear measurements. However, prior knowledge of the sparsity basis is…

Support recovery of sparse signals from compressed linear measurements is a fundamental problem in compressed sensing (CS). In this paper, we study the orthogonal matching pursuit (OMP) algorithm for the recovery of support under noise. We…

We tackle the multi-party speech recovery problem through modeling the acoustic of the reverberant chambers. Our approach exploits structured sparsity models to perform room modeling and speech recovery. We propose a scheme for…

In the context of compressed sensing (CS), this paper considers the problem of reconstructing sparse signals with the aid of other given correlated sources as multiple side information. To address this problem, we theoretically study a…

This article presents novel results concerning the recovery of signals from undersampled data in the common situation where such signals are not sparse in an orthonormal basis or incoherent dictionary, but in a truly redundant dictionary.…

We provide another framework of iterative algorithms based on thresholding, feedback and null space tuning for sparse signal recovery arising in sparse representations and compressed sensing. Several thresholding algorithms with various…

In this paper, we consider the problem of recovering compressively sensed ultrasound images. We build on prior work, and consider a number of existing approaches that we consider to be the state-of-the-art. The methods we consider take…

In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…