Related papers: Perfect Recovery Conditions For Non-Negative Spars…
We investigate non-negative least squares (NNLS) for the recovery of sparse non-negative vectors from noisy linear and biased measurements. We build upon recent results from [1] showing that for matrices whose row-span intersects the…
In this paper we present a linear programming solution for sign pattern recovery of a sparse signal from noisy random projections of the signal. We consider two types of noise models, input noise, where noise enters before the random…
Signal processing is rich in inherently continuous and often nonlinear applications, such as spectral estimation, optical imaging, and super-resolution microscopy, in which sparsity plays a key role in obtaining state-of-the-art results.…
The theory of Compressed Sensing, the emerging sampling paradigm 'that goes against the common wisdom', asserts that 'one can recover signals in Rn from far fewer samples or measurements, if the signal has a sparse representation in some…
This paper provides novel results for the recovery of signals from undersampled measurements based on analysis $\ell_1$-minimization, when the analysis operator is given by a frame. We both provide so-called uniform and nonuniform recovery…
We consider the problem of recovering fusion frame sparse signals from incomplete measurements. These signals are composed of a small number of nonzero blocks taken from a family of subspaces. First, we show that, by using a-priori…
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…
Compressive sensing predicts that sufficiently sparse vectors can be recovered from highly incomplete information. Efficient recovery methods such as $\ell_1$-minimization find the sparsest solution to certain systems of equations. Random…
We consider the following signal recovery problem: given a measurement matrix $\Phi\in \mathbb{R}^{n\times p}$ and a noisy observation vector $c\in \mathbb{R}^{n}$ constructed from $c = \Phi\theta^* + \epsilon$ where $\epsilon\in…
Signals sparse in a transformation domain can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Simple re- construction algorithms are presented in the first part of the paper. The…
The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…
The topic of recovery of a structured model given a small number of linear observations has been well-studied in recent years. Examples include recovering sparse or group-sparse vectors, low-rank matrices, and the sum of sparse and low-rank…
We study the information-theoretic limits of exactly recovering the support of a sparse signal using noisy projections defined by various classes of measurement matrices. Our analysis is high-dimensional in nature, in which the number of…
The problem of detecting the sparsity pattern of a k-sparse vector in R^n from m random noisy measurements is of interest in many areas such as system identification, denoising, pattern recognition, and compressed sensing. This paper…
The sparse signal recovery in the standard compressed sensing (CS) problem requires that the sensing matrix be known a priori. Such an ideal assumption may not be met in practical applications where various errors and fluctuations exist in…
This article considers recovery of signals that are sparse or approximately sparse in terms of a (possibly) highly overcomplete and coherent tight frame from undersampled data corrupted with additive noise. We show that the properly…
Recovering an unknown but structured signal from its measurements is a challenging problem with significant applications in fields such as imaging restoration, wireless communications, and signal processing. In this paper, we consider the…
Compressed sensing (sparse signal recovery) often encounters nonnegative data (e.g., images). Recently we developed the methodology of using (dense) Compressed Counting for recovering nonnegative K-sparse signals. In this paper, we adopt…
In the problem of learning mixtures of linear regressions, the goal is to learn a collection of signal vectors from a sequence of (possibly noisy) linear measurements, where each measurement is evaluated on an unknown signal drawn uniformly…
Recovering the support of sparse vectors in underdetermined linear regression models, \textit{aka}, compressive sensing is important in many signal processing applications. High SNR consistency (HSC), i.e., the ability of a support recovery…