Related papers: Performance bounds for expander-based compressed s…

In this paper, we study the problem of compressed sensing using binary measurement matrices and $\ell_1$-norm minimization (basis pursuit) as the recovery algorithm. We derive new upper and lower bounds on the number of measurements to…

In this paper, compressed sensing with noisy measurements is addressed. The theoretically optimal reconstruction error is studied by evaluating Tanaka's equation. The main contribution is to show that in several regions, which have…

Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…

The purpose of this paper is twofold. The first is to point out that the Restricted Isometry Property (RIP) does not hold in many applications where compressed sensing is successfully used. This includes fields like Magnetic Resonance…

Many applications have benefited remarkably from low-dimensional models in the recent decade. The fact that many signals, though high dimensional, are intrinsically low dimensional has given the possibility to recover them stably from a…

Compressed sensing provides an efficient framework for reconstructing wave signals from reduced measurements. For multi-channel buoy data, the three displacement components exhibit intrinsic correlations, as wave motion contributes…

In this paper, we present a novel yet simple homotopy proximal mapping algorithm for compressive sensing. The algorithm adopts a simple proximal mapping of the $\ell_1$ norm at each iteration and gradually reduces the regularization…

Compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quantification analysis of expensive and high-dimensional physical models. We perform…

We consider the scenario in which multiple sensors send spatially correlated data to a fusion center (FC) via independent Rayleigh-fading channels with additive noise. Assuming that the sensor data is sparse in some basis, we show that the…

We present a mathematical model for communication subject to both network interference and noise. We introduce a framework where the interferers are scattered according to a spatial Poisson process, and are operating asynchronously in a…

Compressed sensing is the art of reconstructing a sparse vector from its inner products with respect to a small set of randomly chosen measurement vectors. It is usually assumed that the ensemble of measurement vectors is in isotropic…

In this paper we develop a general theory of compressed sensing for analog signals, in close similarity to prior results for vectors in finite dimensional spaces that are sparse in a given orthonormal basis. The signals are modeled by…

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.…

Sparse linear inverse problems appear in a variety of settings, but often the noise contaminating observations cannot accurately be described as bounded by or arising from a Gaussian distribution. Poisson observations in particular are a…

Compressed sensing has shown that it is possible to reconstruct sparse high dimensional signals from few linear measurements. In many cases, the solution can be obtained by solving an L1-minimization problem, and this method is accurate…

Can compression algorithms be employed for recovering signals from their underdetermined set of linear measurements? Addressing this question is the first step towards applying compression algorithms for compressed sensing (CS). In this…

Optimizing the acquisition matrix is useful for compressed sensing of signals that are sparse in overcomplete dictionaries, because the acquisition matrix can be adapted to the particular correlations of the dictionary atoms. In this paper…

This paper addresses the topic of robust Bayesian compressed sensing over finite fields. For stationary and ergodic sources, it provides asymptotic (with the size of the vector to estimate) necessary and sufficient conditions on the number…

In this paper, we combat the problem of performance optimization in wireless sensor networks. Specifically, a novel framework is proposed to handle two major research issues. Firstly, we optimize the utilization of resources available to…

As shown in [Blumensath and Davies 2009, Baraniuk et al. 2010], signals whose wavelet coefficients exhibit a rooted tree structure can be recovered using specially-adapted compressed sensing algorithms from just n=O(k) measurements, where k…