Related papers: Compressive Sensing over the Grassmann Manifold: a…
In phase-only compressive sensing (PO-CS), our goal is to recover low-complexity signals (e.g., sparse signals, low-rank matrices) from the phase of complex linear measurements. While perfect recovery of signal direction in PO-CS was…
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 compressive sensing, sparse signals are recovered from underdetermined noisy linear observations. One of the interesting problems which attracted a lot of attention in recent times is the support recovery or sparsity pattern recovery…
We study the compressed sensing (CS) signal estimation problem where an input signal is measured via a linear matrix multiplication under additive noise. While this setup usually assumes sparsity or compressibility in the input signal…
Recent research has shown that performance in signal processing tasks can often be significantly improved by using signal models based on sparse representations, where a signal is approximated using a small number of elements from a fixed…
Fusion frames are collection of subspaces which provide a redundant representation of signal spaces. They generalize classical frames by replacing frame vectors with frame subspaces. This paper considers the sparse recovery of a signal from…
Compressed Sensing (CS) is an effective approach to reduce the required number of samples for reconstructing a sparse signal in an a priori basis, but may suffer severely from the issue of basis mismatch. In this paper we study the problem…
Motivated by the observation that a given signal $\boldsymbol{x}$ admits sparse representations in multiple dictionaries $\boldsymbol{\Psi}_d$ but with varying levels of sparsity across dictionaries, we propose two new algorithms for the…
In this work, we consider the problem of recovering analysis-sparse signals from under-sampled measurements when some prior information about the support is available. We incorporate such information in the recovery stage by suitably tuning…
We consider the problem of exact recovery of a $k$-sparse binary vector from generalized linear measurements (such as logistic regression). We analyze the linear estimation algorithm (Plan, Vershynin, Yudovina, 2017), and also show…
Compressed sensing (CS) provides an elegant framework for recovering sparse signals from compressed measurements. For example, CS can exploit the structure of natural images and recover an image from only a few random measurements. CS is…
We consider the problem of exact support recovery of sparse signals via noisy measurements. The main focus is the sufficient and necessary conditions on the number of measurements for support recovery to be reliable. By drawing an analogy…
We are motivated by problems that arise in a number of applications such as Online Marketing and Explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…
We study the recovery conditions of weighted mixed $\ell_2/\ell_p\,(0<p\leq 1)$ minimization for block sparse signal reconstruction from compressed measurements when partial block support information is available. We show that the block…
This work explores the fundamental problem of the recoverability of a sparse tensor being reconstructed from its compressed embodiment. We present a generalized model of block-sparse tensor recovery as a theoretical foundation, where…
We consider scattered data approximation in samplet coordinates with $\ell_1$-regularization. The application of an $\ell_1$-regularization term enforces sparsity of the coefficients with respect to the samplet basis. Samplets are…
In many real-world problems, recovering sparse signals from underdetermined linear systems remains a fundamental challenge. Although $\ell_1$ norm minimization is widely used, it suffers from estimation bias that prevents it from reaching…
Recovering a sparse signal from an undersampled set of random linear measurements is the main problem of interest in compressed sensing. In this paper, we consider the case where both the signal and the measurements are complex. We study…
An algorithmic framework, based on the difference of convex functions algorithm (DCA), is proposed for minimizing a class of concave sparse metrics for compressed sensing problems. The resulting algorithm iterates a sequence of $\ell_1$…
In this paper we revisit under-determined linear systems of equations with sparse solutions. As is well known, these systems are among core mathematical problems of a very popular compressed sensing field. The popularity of the field as…