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This paper considers the problem of recovering a structured signal from a relatively small number of noisy measurements with the aid of a similar signal which is known beforehand. We propose a new approach to integrate prior information…
This paper proposes a general framework to design a sparse sensing matrix $\ensuremath{\mathbf{A}}\in \mathbb{R}^{m\times n}$, in a linear measurement system $\ensuremath{\mathbf{y}} = \ensuremath{\mathbf{Ax}}^{\natural} +…
Compressed sensing is a signal processing scheme that reconstructs high-dimensional sparse signals from a limited number of observations. In recent years, various problems involving signals with a finite number of discrete values have been…
The purpose of this paper is to report on recent approaches to reconstruction problems based on analog, or in other words, infinite-dimensional, image and signal models. We describe three main contributions to this problem. First, linear…
Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a limited number of noisy linear measurements is an important problem in compressed sensing. In the high-dimensional setting, it is known that recovery with a…
We derive a method to reconstruct Gaussian signals from linear measurements with Gaussian noise. This new algorithm is intended for applications in astrophysics and other sciences. The starting point of our considerations is the principle…
We consider the problem of estimating the support of a vector $\beta^* \in \mathbb{R}^{p}$ based on observations contaminated by noise. A significant body of work has studied behavior of $\ell_1$-relaxations when applied to measurement…
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…
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…
Efficient estimation of wideband spectrum is of great importance for applications such as cognitive radio. Recently, sub-Nyquist sampling schemes based on compressed sensing have been proposed to greatly reduce the sampling rate. However,…
This article introduces a new signal analysis method, which can be interpreted as a principal component analysis in sparse decomposition of the signal. The method, called principal basis analysis, is based on a novel criterion:…
This paper focuses on the estimation of low-complexity signals when they are observed through $M$ uniformly quantized compressive observations. Among such signals, we consider 1-D sparse vectors, low-rank matrices, or compressible signals…
Recent breakthrough results in compressive sensing (CS) have established that many high dimensional signals can be accurately recovered from a relatively small number of non-adaptive linear observations, provided that the signals possess a…
We present a new recovery analysis for a standard compressed sensing algorithm, Iterative Hard Thresholding (IHT) (Blumensath and Davies, 2008), which considers the fixed points of the algorithm. In the context of arbitrary measurement…
Compressive sensing is a technique to sample signals well below the Nyquist rate using linear measurement operators. In this paper we present an algorithm for signal reconstruction given such a set of measurements. This algorithm…
Compressive Sensing, as an emerging technique in signal processing is reviewed in this paper together with its common applications. As an alternative to the traditional signal sampling, Compressive Sensing allows a new acquisition strategy…
The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be useful in this context, the error quantities must be explicit in…
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…
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…