Related papers: Exact Recovery Conditions for Sparse Representatio…
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…
Many applications concern sparse signals, for example, detecting anomalies from the differences between consecutive images taken by surveillance cameras. This paper focuses on the problem of recovering a K-sparse signal x in N dimensions.…
We propose novel necessary and sufficient conditions for a sensing matrix to be "$s$-good" - to allow for exact $\ell_1$-recovery of sparse signals with $s$ nonzero entries when no measurement noise is present. Then we express the error…
Orthogonal matching pursuit (OMP) is a greedy algorithm widely used for the recovery of sparse signals from compressed measurements. In this paper, we analyze the number of iterations required for the OMP algorithm to perform exact recovery…
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…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown…
Sparse signals (i.e., vectors with a small number of non-zero entries) build the foundation of most kernel (or nullspace) results, uncertainty relations, and recovery guarantees in the sparse signal processing and compressive sensing…
This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements -- L_1-minimization methods and iterative methods (Matching Pursuits). We find a simple regularized…
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…
We study the problem of recovering a hidden binary $k$-sparse $p$-dimensional vector $\beta$ from $n$ noisy linear observations $Y=X\beta+W$ where $X_{ij}$ are i.i.d. $\mathcal{N}(0,1)$ and $W_i$ are i.i.d. $\mathcal{N}(0,\sigma^2)$. A…
High-dimensional data often lie in low-dimensional subspaces corresponding to different classes they belong to. Finding sparse representations of data points in a dictionary built using the collection of data helps to uncover…
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…
The goal of phaseless compressed sensing is to recover an unknown sparse or approximately sparse signal from the magnitude of its measurements. However, it does not take advantage of any support information of the original signal.…
We study distributed schemes for high-dimensional sparse linear regression, based on orthogonal matching pursuit (OMP). Such schemes are particularly suited for settings where a central fusion center is connected to end machines, that have…
We demonstrate a simple greedy algorithm that can reliably recover a d-dimensional vector v from incomplete and inaccurate measurements x. Here our measurement matrix is an N by d matrix with N much smaller than d. Our algorithm,…
This article considers the recovery of low-rank matrices via a convex nuclear-norm minimization problem and presents two null space properties (NSP) which characterize uniform recovery for the case of block-diagonal matrices and…
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…
In this work, we study the problem of learning a nonlinear dynamical system by parameterizing its dynamics using basis functions. We assume that disturbances occur at each time step with an arbitrary probability $p$, which models the…
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 problem of recovering a partially sparse solution of an underdetermined system of linear equations by minimizing the $\ell_1$-norm of the part of the solution vector which is known to be sparse. Such a problem is closely…