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We investigate conditions for the unique recoverability of sparse integer-valued signals from a small number of linear measurements. Both the objective of minimizing the number of nonzero components, the so-called $\ell_0$-norm, as well as…
As a paradigm to recover the sparse signal from a small set of linear measurements, compressed sensing (CS) has stimulated a great deal of interest in recent years. In order to apply the CS techniques to wireless communication systems,…
We address the problem of Compressed Sensing (CS) with side information. Namely, when reconstructing a target CS signal, we assume access to a similar signal. This additional knowledge, the side information, is integrated into CS via L1-L1…
Compressive sensing (CS) is an alternative to Shannon/Nyquist sampling for the acquisition of sparse or compressible signals that can be well approximated by just K << N elements from an N-dimensional basis. Instead of taking periodic…
In this paper, we consider the problem of sparse signal detection based on partial support set estimation with compressive measurements in a distributed network. Multiple nodes in the network are assumed to observe sparse signals which…
In this paper, we study the recovery of a signal from a set of noisy linear projections (measurements), when such projections are unlabeled, that is, the correspondence between the measurements and the set of projection vectors (i.e., the…
The Compressive Sensing (CS) as a novel acquisition approach that finds its usage in image processing. The hypothesis like this one assures signal recovery with high quality from decreased number of samples compared with the number required…
Too high sampling rate is the bottleneck to wideband spectrum sensing for cognitive radio in mobile communication. Compressed sensing (CS) is introduced to transfer the sampling burden. The standard sparse signal recovery of CS does not…
We derive an information-theoretic lower bound for sample complexity in sparse recovery problems where inputs can be chosen sequentially and adaptively. This lower bound is in terms of a simple mutual information expression and unifies many…
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…
Most of compressed sensing (CS) theory to date is focused on incoherent sensing, that is, columns from the sensing matrix are highly uncorrelated. However, sensing systems with naturally occurring correlations arise in many applications,…
In the theory of compressed sensing (CS), the sparsity $\|x\|_0$ of the unknown signal $\mathbf{x} \in \mathcal{R}^n$ is of prime importance and the focus of reconstruction algorithms has mainly been either $\|x\|_0$ or its convex…
Compressed sensing is a paradigm within signal processing that provides the means for recovering structured signals from linear measurements in a highly efficient manner. Originally devised for the recovery of sparse signals, it has become…
This paper presents a tutorial for CS applications in communications networks. The Shannon's sampling theorem states that to recover a signal, the sampling rate must be as least the Nyquist rate. Compressed sensing (CS) is based on the…
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…
Compressive sensing has shown significant promise in biomedical fields. It reconstructs a signal from sub-Nyquist random linear measurements. Classical methods only exploit the sparsity in one domain. A lot of biomedical signals have…
The paper introduces a framework for the recoverability analysis in compressive sensing for imaging applications such as CI cameras, rapid MRI and coded apertures. This is done using the fact that the Spherical Section Property (SSP) of a…
Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…
This article extends the concept of compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a…
Compressive sensing is a signal acquisition framework based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable recovery. In this paper we introduce a new theory for…