Related papers: Nullspace Property for Optimality of Minimum Frame…
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 present a new coherence-based performance guarantee for the Orthogonal Matching Pursuit (OMP) algorithm. An upper bound for the probability of correctly identifying the support of a sparse signal with additive white…
In the blind deconvolution problem, we observe the convolution of an unknown filter and unknown signal and attempt to reconstruct the filter and signal. The problem seems impossible in general, since there are seemingly many more unknowns…
Successful applications of sparse models in computer vision and machine learning imply that in many real-world applications, high dimensional data is distributed in a union of low dimensional subspaces. Nevertheless, the underlying…
This paper introduces the sparsifying preconditioner for the pseudospectral approximation of highly indefinite systems on periodic structures, which include the frequency-domain response problems of the Helmholtz equation and the…
We consider the problem of recovering an unknown effectively $(s_1,s_2)$-sparse low-rank-$R$ matrix $X$ with possibly non-orthogonal rank-$1$ decomposition from incomplete and inaccurate linear measurements of the form $y = \mathcal A (X) +…
In this paper, we consider a compressed sensing problem of reconstructing a sparse signal from an undersampled set of noisy linear measurements. The regularized least squares or least absolute shrinkage and selection operator (LASSO)…
In this note, we investigate the theoretical properties of Orthogonal Matching Pursuit (OMP), a class of decoder to recover sparse signal in compressed sensing. In particular, we show that the OMP decoder can give $(p,q)$ instance…
The goal of compressed sensing is to reconstruct a sparse signal under a few linear measurements far less than the dimension of the ambient space of the signal. However, many real-life applications in physics and biomedical sciences carry…
The problem of multiple sensors simultaneously acquiring measurements of a single object can be found in many applications. In this paper, we present the optimal recovery guarantees for the recovery of compressible signals from multi-sensor…
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…
We consider the problem of recovering a matrix from its action on a known vector in the setting where the matrix can be represented efficiently in a known matrix dictionary. Connections with sparse signal recovery allows for the use of…
We address the non-convex optimisation problem of finding a sparse matrix on the Stiefel manifold (matrices with mutually orthogonal columns of unit length) that maximises (or minimises) a quadratic objective function. Optimisation problems…
This paper considers the design of tunable decision schemes capable of rejecting with high probability mismatched signals embedded in Gaussian interference with unknown covariance matrix. To this end, a sparse recovery technique is…
Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of…
In this paper, we consider the sparse phase retrieval problem, recovering an $s$-sparse signal $\bm{x}^{\natural}\in\mathbb{R}^n$ from $m$ phaseless samples $y_i=|\langle\bm{x}^{\natural},\bm{a}_i\rangle|$ for $i=1,\ldots,m$. Existing…
A greedy pursuit strategy which finds a common basis for approximating a set of similar signals is proposed. The strategy extends the Optimized Orthogonal Matching Pursuit approach to selecting the subspace containing the approximation of…
Many scientific and engineering applications feature nonsmooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the nonsmooth objective is equipped with…
Support recovery of sparse signals from noisy measurements with orthogonal matching pursuit (OMP) has been extensively studied. In this paper, we show that for any $K$-sparse signal $\x$, if a sensing matrix $\A$ satisfies the restricted…
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…