Related papers: Reduce and Boost: Recovering Arbitrary Sets of Joi…
We present and analyze a novel sparse polynomial technique for approximating high-dimensional Hilbert-valued functions, with application to parameterized partial differential equations (PDEs) with deterministic and stochastic inputs. Our…
Compressed sensing (sparse signal recovery) often encounters nonnegative data (e.g., images). Recently we developed the methodology of using (dense) Compressed Counting for recovering nonnegative K-sparse signals. In this paper, we adopt…
Motivated by applications such as sparse PCA, in this paper we present provably-accurate one-pass algorithms for the sparse approximation of the top eigenvectors of extremely massive matrices based on a single compact linear sketch. The…
We consider the problem of recovering elements of a low-dimensional model from linear measurements. From signal and image processing to inverse problems in data science, this question has been at the center of many applications. Lately,…
It is well known that the performance of sparse vector recovery algorithms from compressive measurements can depend on the distribution underlying the non-zero elements of a sparse vector. However, the extent of these effects has yet to be…
We study the problem of jointly sparse support recovery with 1-bit compressive measurements in a sensor network. Sensors are assumed to observe sparse signals having the same but unknown sparse support. Each sensor quantizes its measurement…
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…
We address the problem of recovering a sparse $n$-vector within a given subspace. This problem is a subtask of some approaches to dictionary learning and sparse principal component analysis. Hence, if we can prove scaling laws for recovery…
Frequency recovery/estimation from discrete samples of superimposed sinusoidal signals is a classic yet important problem in statistical signal processing. Its research has recently been advanced by atomic norm techniques which exploit…
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…
Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…
The problem of finding the sparsest vector (direction) in a low dimensional subspace can be considered as a homogeneous variant of the sparse recovery problem, which finds applications in robust subspace recovery, dictionary learning,…
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…
One-bit compressed sensing (1bCS) is an extreme-quantized signal acquisition method that has been intermittently studied in the past decade. In 1bCS, linear samples of a high dimensional signal are quantized to only one bit per sample (sign…
Joint sparsity has attracted considerable attention in recent years in many fields including sparse signal recovery in compressed sensing (CS), statistics, and machine learning. Traditional convex models suffer from the suboptimal…
In this paper we theoretically study exact recovery of sparse vectors from compressed measurements by minimizing a general nonconvex function that can be decomposed into the sum of single variable functions belonging to a class of smooth…
This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional…
Inspired by recent work on convex formulations of clustering (Lashkari & Golland, 2008; Nowozin & Bakir, 2008) we investigate a new formulation of the Sparse Coding Problem (Olshausen & Field, 1997). In sparse coding we attempt to…
In this paper, we propose \textit{coded compressive sensing} that recovers an $n$-dimensional integer sparse signal vector from a noisy and quantized measurement vector whose dimension $m$ is far-fewer than $n$. The core idea of coded…
One-bit compressed sensing (1bCS) is an extremely quantized signal acquisition method that has been proposed and studied rigorously in the past decade. In 1bCS, linear samples of a high dimensional signal are quantized to only one bit per…