Related papers: Covering point-sets with parallel hyperplanes and …
Recent work in compressed sensing theory shows that $n\times N$ independent and identically distributed (IID) sensing matrices whose entries are drawn independently from certain probability distributions guarantee exact recovery of a sparse…
Motivated by the problem of integer sparse recovery we study the following question. Let $A$ be an $m \times d$ integer matrix whose entries are in absolute value at most $k$. How large can be $d=d(m,k)$ if all $m \times m$ submatrices of…
The choice of the sensing matrix is crucial in compressed sensing. Random Gaussian sensing matrices satisfy the restricted isometry property, which is crucial for solving the sparse recovery problem using convex optimization techniques.…
We give a new, very general, formulation of the compressed sensing problem in terms of coordinate projections of an analytic variety, and derive sufficient sampling rates for signal reconstruction. Our bounds are linear in the coherence of…
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…
The topic of recovery of a structured model given a small number of linear observations has been well-studied in recent years. Examples include recovering sparse or group-sparse vectors, low-rank matrices, and the sum of sparse and low-rank…
We consider the extensively studied problem of $\ell_2/\ell_2$ compressed sensing. The main contribution of our work is an improvement over [Gilbert, Li, Porat and Strauss, STOC 2010] with faster decoding time and significantly smaller…
We study sparse recovery with structured random measurement matrices having independent, identically distributed, and uniformly bounded rows and with a nontrivial covariance structure. This class of matrices arises from random sampling of…
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 this paper, motivated by network inference and tomography applications, we study the problem of compressive sensing for sparse signal vectors over graphs. In particular, we are interested in recovering sparse vectors representing the…
Parallel acquisition systems arise in various applications in order to moderate problems caused by insufficient measurements in single-sensor systems. These systems allow simultaneous data acquisition in multiple sensors, thus alleviating…
We construct two families of deterministic sensing matrices where the columns are obtained by exponentiating codewords in the quaternary Delsarte-Goethals code $DG(m,r)$. This method of construction results in sensing matrices with low…
This paper is concerned with estimating the column space of an unknown low-rank matrix $\boldsymbol{A}^{\star}\in\mathbb{R}^{d_{1}\times d_{2}}$, given noisy and partial observations of its entries. There is no shortage of scenarios where…
Compressed sensing seeks to recover a sparse vector from a small number of linear and non-adaptive measurements. While most work so far focuses on Gaussian or Bernoulli random measurements we investigate the use of partial random circulant…
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…
Consider the problem of recovering an unknown signal from undersampled measurements, given the knowledge that the signal has a sparse representation in a specified dictionary $D$. This problem is now understood to be well-posed and…
Deep networks can be trained to map images into a low-dimensional latent space. In many cases, different images in a collection are articulated versions of one another; for example, same object with different lighting, background, or pose.…
We propose a robust and efficient approach to the problem of compressive phase retrieval in which the goal is to reconstruct a sparse vector from the magnitude of a number of its linear measurements. The proposed framework relies on…
Sparse binary matrices are of great interest in the field of sparse recovery, nonnegative compressed sensing, statistics in networks, and theoretical computer science. This class of matrices makes it possible to perform signal recovery with…
In compressed sensing, a small number of linear measurements can be used to reconstruct an unknown signal. Existing approaches leverage assumptions on the structure of these signals, such as sparsity or the availability of a generative…