Related papers: Weighted $\ell_1$-minimization for generalized non…
This work considers recovery of signals that are sparse over two bases. For instance, a signal might be sparse in both time and frequency, or a matrix can be low rank and sparse simultaneously. To facilitate recovery, we consider minimizing…
This paper study recovery conditions of weighted L1 minimization for signal reconstruction from compressed sensing measurements. A sufficient condition for exact recovery by using the general weighted L1 minimization is derived, which…
This paper investigates the problem of recovering the support of structured signals via adaptive compressive sensing. We examine several classes of structured support sets, and characterize the fundamental limits of accurately recovering…
In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a…
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…
Compressed sensing with subsampled unitary matrices benefits from \emph{optimized} sampling schemes, which feature improved theoretical guarantees and empirical performance relative to uniform subsampling. We provide, in a first of its kind…
We propose to reduce the original well-posed problem of compressive sensing to weighted-MAX-SAT. Compressive sensing is a novel randomized data acquisition approach that linearly samples sparse or compressible signals at a rate much below…
Compressed sensing is a promising technique that attempts to faithfully recover sparse signal with as few linear and nonadaptive measurements as possible. Its performance is largely determined by the characteristic of sensing matrix.…
This letter proposes a novel distributed compressed estimation scheme for sparse signals and systems based on compressive sensing techniques. The proposed scheme consists of compression and decompression modules inspired by compressive…
We present improved sampling complexity bounds for stable and robust sparse recovery in compressed sensing. Our unified analysis based on l1 minimization encompasses the case where (i) the measurements are block-structured samples in order…
Many practical sensing applications involve multiple sensors simultaneously acquiring measurements of a single object. Conversely, most existing sparse recovery guarantees in compressed sensing concern only single-sensor acquisition…
The sparse optimization problems arise in many areas of science and engineering, such as compressed sensing, image processing, statistical and machine learning. The $\ell_{0}$-minimization problem is one of such optimization problems, which…
We introduce and analyze a framework for function interpolation using compressed sensing. This framework - which is based on weighted $\ell^1$ minimization - does not require a priori bounds on the expansion tail in either its…
The $\ell^0$ minimization of compressed sensing is often relaxed to $\ell^1$, which yields easy computation using the shrinkage mapping known as soft thresholding, and can be shown to recover the original solution under certain hypotheses.…
This paper aims to build an estimate of an unknown density of the data with measurement error as a linear combination of functions from a dictionary. Inspired by the penalization approach, we propose the weighted Elastic-net penalized…
For Gaussian sampling matrices, we provide bounds on the minimal number of measurements $m$ required to achieve robust weighted sparse recovery guarantees in terms of how well a given prior model for the sparsity support aligns with the…
The recovery of signals with finite-valued components from few linear measurements is a problem with widespread applications and interesting mathematical characteristics. In the compressed sensing framework, tailored methods have been…
We discuss a general notion of "sparsity structure" and associated recoveries of a sparse signal from its linear image of reduced dimension possibly corrupted with noise. Our approach allows for unified treatment of (a) the "usual sparsity"…
We consider the problem of estimating the support of a vector $\beta^* \in \mathbb{R}^{p}$ based on observations contaminated by noise. A significant body of work has studied behavior of $\ell_1$-relaxations when applied to measurement…
In this paper, we investigate the theoretical guarantees of penalized $\lun$ minimization (also called Basis Pursuit Denoising or Lasso) in terms of sparsity pattern recovery (support and sign consistency) from noisy measurements with…