Related papers: Sparse Signal Recovery from Random Measurements
Motivated by applications in unsourced random access, this paper develops a novel scheme for the problem of compressed sensing of binary signals. In this problem, the goal is to design a sensing matrix $A$ and a recovery algorithm, such…
The task of compressed sensing is to recover a sparse vector from a small number of linear and non-adaptive measurements, and the problem of finding a suitable measurement matrix is very important in this field. While most recent works…
In this paper we consider a system of quadratic equations |<z_j, x>|^2 = b_j, j = 1, ..., m, where x in R^n is unknown while normal random vectors z_j in R_n and quadratic measurements b_j in R are known. The system is assumed to be…
We study the use of very sparse random projections for compressed sensing (sparse signal recovery) when the signal entries can be either positive or negative. In our setting, the entries of a Gaussian design matrix are randomly sparsified…
Compressed sensing is a technique for recovering an unknown sparse signal from a small number of linear measurements. When the measurement matrix is random, the number of measurements required for perfect recovery exhibits a phase…
A compressed sensing method consists of a rectangular measurement matrix, $M \in \mathbbm{R}^{m \times N}$ with $m \ll N$, together with an associated recovery algorithm, $\mathcal{A}: \mathbbm{R}^m \rightarrow \mathbbm{R}^N$. Compressed…
We improve existing results in the field of compressed sensing and matrix completion when sampled data may be grossly corrupted. We introduce three new theorems. 1) In compressed sensing, we show that if the m \times n sensing matrix has…
We study the support recovery problem for compressed sensing, where the goal is to reconstruct the a high-dimensional $K$-sparse signal $\mathbf{x}\in\mathbb{R}^N$, from low-dimensional linear measurements with and without noise. Our key…
In the context of the compressed sensing problem, we propose a new ensemble of sparse random matrices which allow one (i) to acquire and compress a {\rho}0-sparse signal of length N in a time linear in N and (ii) to perfectly recover the…
In this paper we study the compressed sensing problem of recovering a sparse signal from a system of underdetermined linear equations when we have prior information about the probability of each entry of the unknown signal being nonzero. In…
Recovery of support of a sparse vector from simple measurements is a widely-studied problem, considered under the frameworks of compressed sensing, 1-bit compressed sensing, and more general single index models. We consider generalizations…
We consider the problem of recovering signals from their power spectral density. This is a classical problem referred to in literature as the phase retrieval problem, and is of paramount importance in many fields of applied sciences. In…
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 describe a probabilistic, {\it sublinear} runtime, measurement-optimal system for model-based sparse recovery problems through dimensionality reducing, {\em dense} random matrices. Specifically, we obtain a linear sketch $u\in \R^M$ of a…
The goal of compressed sensing is to estimate a vector from an underdetermined system of noisy linear measurements, by making use of prior knowledge on the structure of vectors in the relevant domain. For almost all results in this…
We consider the recovery of a nonnegative vector x from measurements y = Ax, where A is an m-by-n matrix whos entries are in {0, 1}. We establish that when A corresponds to the adjacency matrix of a bipartite graph with sufficient…
Motivated by the settings where sensing the entire tensor is infeasible, this paper proposes a novel tensor compressed sensing model, where measurements are only obtained from sensing each lateral slice via mutually independent matrices.…
This article extends the concept of compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a…
We give the first computationally tractable and almost optimal solution to the problem of one-bit compressed sensing, showing how to accurately recover an s-sparse vector x in R^n from the signs of O(s log^2(n/s)) random linear measurements…
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…