Related papers: Probabilistic Recovery Guarantees for Sparsely Cor…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
Sparse Principal Component Analysis (PCA) is a prevalent tool across a plethora of subfields of applied statistics. While several results have characterized the recovery error of the principal eigenvectors, these are typically in spectral…
This paper considers the problem of recovering a structured signal from a relatively small number of noisy measurements with the aid of a similar signal which is known beforehand. We propose a new approach to integrate prior information…
Recovery of arbitrarily positioned samples that are missing in sparse signals recently attracted significant research interest. Sparse signals with heavily corrupted arbitrary positioned samples could be analyzed in the same way as…
This paper addresses the problem of sparse phase retrieval, a fundamental inverse problem in applied mathematics, physics, and engineering, where a signal need to be reconstructed using only the magnitude of its transformation while phase…
From a numerical analysis perspective, assessing the robustness of l1-minimization is a fundamental issue in compressed sensing and sparse regularization. Yet, the recovery guarantees available in the literature usually depend on a priori…
One-bit compressive sensing has extended the scope of sparse recovery by showing that sparse signals can be accurately reconstructed even when their linear measurements are subject to the extreme quantization scenario of binary…
This work treats the recovery of sparse, binary signals through box-constrained basis pursuit using biased measurement matrices. Using a probabilistic model, we provide conditions under which the recovery of both sparse and saturated binary…
This paper introduces a simple and very general theory of compressive sensing. In this theory, the sensing mechanism simply selects sensing vectors independently at random from a probability distribution F; it includes all models - e.g.…
Compressed sensing and its extensions have recently triggered interest in randomized signal acquisition. A key finding is that random measurements provide sparse signal reconstruction guarantees for efficient and stable algorithms with a…
This paper considers the problem of recovering a one or two dimensional discrete signal which is approximately sparse in its discrete gradient from an incomplete subset of its discrete Fourier coefficients which have been corrupted with…
It is well known that $\ell_1$ minimization can be used to recover sufficiently sparse unknown signals from compressed linear measurements. In fact, exact thresholds on the sparsity, as a function of the ratio between the system dimensions,…
We consider the problem of recovering the support of a sparse signal using noisy projections. While extensive work has been done on the dense measurement matrix setting, the sparse setting remains less explored. In this work, we establish…
In many data acquisition systems it is common to observe signals whose amplitudes have been clipped. We present two new algorithms for recovering a clipped signal by leveraging the model assumption that the underlying signal is sparse in…
A host of problems involve the recovery of structured signals from a dimensionality reduced representation such as a random projection; examples include sparse signals (compressive sensing) and low-rank matrices (matrix completion). Given…
Conventional sparse phase retrieval schemes can recover sparse signals from the magnitude of linear measurements only up to a global phase ambiguity. This work proposes a novel approach that instead utilizes the magnitude of affine…
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…
Compressed sensing is a relatively new mathematical paradigm that shows a small number of linear measurements are enough to efficiently reconstruct a large dimensional signal under the assumption the signal is sparse. Applications for this…
In this paper, we present coherence-based performance guarantees of Orthogonal Matching Pursuit (OMP) for both support recovery and signal reconstruction of sparse signals when the measurements are corrupted by noise. In particular, two…
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…