Related papers: Achieving Optimal Sample Complexity for a Broader …
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
A well-known analysis of Tropp and Gilbert shows that orthogonal matching pursuit (OMP) can recover a k-sparse n-dimensional real vector from 4 k log(n) noise-free linear measurements obtained through a random Gaussian measurement matrix…
The sparsity in levels model recently inspired a new generation of effective acquisition and reconstruction modalities for compressive imaging. Moreover, it naturally arises in various areas of signal processing such as parallel…
We consider the problem of recovering sparse vectors from underdetermined linear measurements via $\ell_p$-constrained basis pursuit. Previous analyses of this problem based on generalized restricted isometry properties have suggested that…
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…
This paper studies sequential methods for recovery of sparse signals in high dimensions. When compared to fixed sample size procedures, in the sparse setting, sequential methods can result in a large reduction in the number of samples…
In this paper, we present new results on using orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries for complex cases (i.e., complex measurement vector, complex dictionary and complex…
Recent results from compressive sampling (CS) have demonstrated that accurate reconstruction of sparse signals often requires far fewer samples than suggested by the classical Nyquist--Shannon sampling theorem. Typically, signal…
Compressed sensing investigates the recovery of sparse signals from linear measurements. But often, in a wide range of applications, one is given only the absolute values (squared) of the linear measurements. Recovering such signals (not…
We investigate conditions for the unique recoverability of sparse integer-valued signals from a small number of linear measurements. Both the objective of minimizing the number of nonzero components, the so-called $\ell_0$-norm, as well as…
This paper develops a novel algorithm, termed \emph{SPARse Truncated Amplitude flow} (SPARTA), to reconstruct a sparse signal from a small number of magnitude-only measurements. It deals with what is also known as sparse phase retrieval…
Sparse signal recovery or compressed sensing can be formulated as certain sparse optimization problems. The classic optimization theory indicates that the Newton-like method often has a numerical advantage over the gradient method for…
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…
Quantifying the complexity and irregularity of time series data is a primary pursuit across various data-scientific disciplines. Sample entropy (SampEn) is a widely adopted metric for this purpose, but its reliability is sensitive to the…
Motivated by the question of optimal functional approximation via compressed sensing, we propose generalizations of the Iterative Hard Thresholding and the Compressive Sampling Matching Pursuit algorithms able to promote sparse in levels…
We introduce a \emph{batch} version of sparse recovery, where the goal is to report a sequence of vectors $A_1',\ldots,A_m' \in \mathbb{R}^n$ that estimate unknown signals $A_1,\ldots,A_m \in \mathbb{R}^n$ using a few linear measurements,…
We study the problem of sampling and reconstructing spectrally sparse graph signals where the objective is to select a subset of nodes of prespecified cardinality that ensures interpolation of the original signal with the lowest possible…
We consider the recovery of sparse signals subject to sparse interference, as introduced in Studer et al., IEEE Trans. IT, 2012. We present novel probabilistic recovery guarantees for this framework, covering varying degrees of knowledge of…
This article aims to provide a comprehensive overview of sparse optimization, with a focus on both sparse signal recovery and sparse regularization techniques. We will begin by exploring the foundations of sparse optimization, delving into…
Compressed sensing aims to undersample certain high-dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a…