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The co-sparse analysis model for signals assumes that the signal of interest can be multiplied by an analysis dictionary \Omega, leading to a sparse outcome. This model stands as an interesting alternative to the more classical synthesis…
We consider high dimensional sparse regression, and develop strategies able to deal with arbitrary -- possibly, severe or coordinated -- errors in the covariance matrix $X$. These may come from corrupted data, persistent experimental…
A novel sparse array synthesis method for non-uniform planar arrays is proposed, which belongs to compressive sensing (CS)-based systhesis. Particularly, we propose an off-grid refinement technique to simultaneously optimize the antenna…
This paper investigates the sparse phase retrieval problem, which aims to recover a sparse signal from a system of quadratic measurements. In this work, we propose a novel non-convex algorithm, termed Gradient Hard Thresholding Pursuit…
We present a novel stagewise strategy for improving greedy algorithms for sparse recovery. We demonstrate its efficiency both for synthesis and analysis sparse priors, where in both cases we demonstrate its computational efficiency and…
Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an $l_0$-constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm…
Compressed sensing is a new data acquisition paradigm enabling universal, simple, and reduced-cost acquisition, by exploiting a sparse signal model. Most notably, recovery of the signal by computationally efficient algorithms is guaranteed…
Sparsity-constrained optimization has wide applicability in machine learning, statistics, and signal processing problems such as feature selection and compressive Sensing. A vast body of work has studied the sparsity-constrained…
Greedy algorithm are in widespread use for sparse recovery because of its efficiency. But some evident flaws exists in most popular greedy algorithms, such as CoSaMP, which includes unreasonable demands on prior knowledge of target signal…
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…
Matrix recovery is the problem of recovering a low-rank matrix from a few linear measurements. Recently, this problem has gained a lot of attention as it is employed in many applications such as Netflix prize problem, seismic data…
The most frequently used condition for sampling matrices employed in compressive sampling is the restricted isometry (RIP) property of the matrix when restricted to sparse signals. At the same time, imposing this condition makes it…
In many compressive sensing problems today, the relationship between the measurements and the unknowns could be nonlinear. Traditional treatment of such nonlinear relationships have been to approximate the nonlinearity via a linear model…
This paper provides a simple proof of the mutual incoherence condition $\mu < \frac{1}{2K-1}$ under which K-sparse signal can be accurately reconstructed from a small number of linear measurements using the orthogonal matching pursuit (OMP)…
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…
Greedy pursuit algorithms (GPAs) are widely used to reconstruct sparse signals. Even though many electromagnetic (EM) inverse scattering problems are solved on sparse investigation domains, GPAs have rarely been used for this purpose. This…
Probabilistic Coalition Structure Generation (PCSG) is NP-hard and can be recast as an $l_0$-type sparse recovery problem by representing coalition structures as sparse coefficient vectors over a coalition-incidence design. A natural…
We consider the problem of estimating a deterministic sparse vector x from underdetermined measurements Ax+w, where w represents white Gaussian noise and A is a given deterministic dictionary. We analyze the performance of three sparse…
Direction of Arrival (DOA) estimation of mixed uncorrelated and coherent sources is a long existing challenge in array signal processing. Application of compressive sensing to array signal processing has opened up an exciting class of…
A novel algorithm for the recovery of low-rank matrices acquired via compressive linear measurements is proposed and analyzed. The algorithm, a variation on the iterative hard thresholding algorithm for low-rank recovery, is designed to…