A well-known analysis of Tropp and Gilbert shows that orthogonal matching pursuit (OMP) can recover a k-sparse n-dimensional real vector from m = 4k log(n) noise-free linear measurements obtained through a random Gaussian measurement matrix with a probability that approaches one as n → ∞. This work strengthens this result by showing that a lower number of measurements, m = 2k log(n − k), is in ...

This paper addresses source separation from a linear mixture under two assumptions: source sparsity and orthogonality of the mixing matrix. We propose efficient sparse separation via a two-stage process. In the first stage we attempt to recover the sparsity pattern of the sources by exploiting the orthogonality prior. In the second stage, the support is used to reformulate the recovery task as ...

Compressive sensing is a method for recording a k-sparse signal x ∈ R with (possibly noisy) linear measurements of the form y = Ax, where A ∈ Rm×n describes the measurement process. Seminal results in compressive sensing show that it is possible to recover the signal x from m = O(k log n k ) measurements and that this is tight. The model-based compressive sensing framework overcomes this lower ...

Lower dimensional signal representation schemes frequently assume that the signal of interest lies in a single vector space. In the context of the recently developed theory of compressive sensing (CS), it is often assumed that the signal of interest is sparse in an orthonormal basis. However, in many practical applications, this requirement may be too restrictive. A generalization of the standa...

In applications such as medical statistics and genetics, we encounter situations where a large number of highly correlated predictors explain a response. For example, the response may be a disease indicator and the predictors may be treatment indicators or single nucleotide polymorphisms (SNPs). Constructing a good predictive model in such cases is well studied. Less well understood is how to r...

A problem that arises in slice-selective magnetic resonance imaging (MRI) radio-frequency (RF) excitation pulse design is abstracted as a novel linear inverse problem with a simultaneous sparsity constraint. Multiple unknown signal vectors are to be determined, where each passes through a different system matrix and the results are added to yield a single observation vector. Given the matrices ...

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 recently found applications in problems such as compressive imaging, multi-sensor acquisition systems and sparse regularization in inverse problems. In this...