Related papers: Hierarchically Block-Sparse Recovery With Prior Su…
Compressed Sensing (CS) is a signal processing technique which can accurately recover sparse signals from linear measurements with far fewer number of measurements than those required by the classical Shannon-Nyquist theorem. Block sparse…
This work explores the fundamental problem of the recoverability of a sparse tensor being reconstructed from its compressed embodiment. We present a generalized model of block-sparse tensor recovery as a theoretical foundation, where…
We consider compressed sensing of block-sparse signals, i.e., sparse signals that have nonzero coefficients occurring in clusters. An uncertainty relation for block-sparse signals is derived, based on a block-coherence measure, which we…
We consider the greedy algorithms for the joint recovery of high-dimensional sparse signals based on the block multiple measurement vector (BMMV) model in compressed sensing (CS). To this end, we first put forth two versions of simultaneous…
This paper concentrates on the recovery of block-sparse signals, which is not only sparse but also nonzero elements are arrayed into some blocks (clusters) rather than being arbitrary distributed all over the vector, from linear…
We consider the problem of recovering block-sparse signals whose structures are unknown \emph{a priori}. Block-sparse signals with nonzero coefficients occurring in clusters arise naturally in many practical scenarios. However, the…
A new family of operators, coined hierarchical measurement operators, is introduced and discussed within the well-known hierarchical sparse recovery framework. Such operator is a composition of block and mixing operations and notably…
Compressed sensing (CS) techniques demand significant storage and computational resources, when recovering high-dimensional sparse signals. Block CS (BCS), a special class of CS, addresses both the storage and complexity issues by…
We consider the block orthogonal multi-matching pursuit (BOMMP) algorithm for the recovery of block sparse signals. A sharp bound is obtained for the exact reconstruction of block $K$-sparse signals via the BOMMP algorithm in the noiseless…
In this paper, we use the block orthogonal matching pursuit (BOMP) algorithm to recover block sparse signals $\x$ from measurements $\y=\A\x+\v$, where $\v$ is an $\ell_2$-bounded noise vector (i.e., $\|\v\|_2\leq \epsilon$ for some…
We consider compressed sensing of block-sparse signals, i.e., sparse signals that have nonzero coefficients occuring in clusters. Based on an uncertainty relation for block-sparse signals, we define a block-coherence measure and we show…
Hierarchically sparse signals and Kronecker product structured measurements arise naturally in a variety of applications. The simplest example of a hierarchical sparsity structure is two-level $(s,\sigma)$-hierarchical sparsity which…
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…
Several exact recovery criteria (ERC) ensuring that orthogonal matching pursuit (OMP) identifies the correct support of sparse signals have been developed in the last few years. These ERC rely on the restricted isometry property (RIP), the…
Support recovery of sparse signals from compressed linear measurements is a fundamental problem in compressed sensing (CS). In this paper, we study the orthogonal matching pursuit (OMP) algorithm for the recovery of support under noise. We…
We study the problem of recovering the sparsity pattern of block-sparse signals from noise-corrupted measurements. A simple, efficient recovery method, namely, a block-version of the orthogonal matching pursuit (OMP) method, is considered…
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…
We propose and analyze a solution to the problem of recovering a block sparse signal with sparse blocks from linear measurements. Such problems naturally emerge inter alia in the context of mobile communication, in order to meet the…
This paper considers the exact recovery of $k$-sparse signals in the noiseless setting and support recovery in the noisy case when some prior information on the support of the signals is available. This prior support consists of two parts.…
In this paper, we consider the recovery of block sparse signals, whose nonzero entries appear in blocks (or clusters) rather than spread arbitrarily throughout the signal, from incomplete linear measurement. A high order sufficient…