Related papers: Compressive Principal Component Pursuit
We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse eigenvalue statistic. Alas, computing this test is known to…
The paper studies the problem of recovering a spectrally sparse object from a small number of time domain samples. Specifically, the object of interest with ambient dimension $n$ is assumed to be a mixture of $r$ complex multi-dimensional…
We study an auto-calibration problem in which a transform-sparse signal is acquired via compressive sensing by multiple sensors in parallel, but with unknown calibration parameters of the sensors. This inverse problem has an important…
We consider robust low rank matrix estimation as a trace regression when outputs are contaminated by adversaries. The adversaries are allowed to add arbitrary values to arbitrary outputs. Such values can depend on any samples. We deal with…
A novel framework to construct an efficient sensing (measurement) matrix, called mixed adaptive-random (MAR) matrix, is introduced for directly acquiring a compressed image representation. The mixed sampling (sensing) procedure hybridizes…
In this paper, we study the problem of matrix recovery, which aims to restore a target matrix of authentic samples from grossly corrupted observations. Most of the existing methods, such as the well-known Robust Principal Component Analysis…
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…
We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of…
In this paper we revisit the sparse multiple measurement vector (MMV) problem where the aim is to recover a set of jointly sparse multichannel vectors from incomplete measurements. This problem has received increasing interest as an…
A novel algorithm for the recovery of low-rank matrices acquired via compressive linear measurements is proposed and analyzed. The algorithm, a variation on the iterative hard thresholding algorithm for low-rank recovery, is designed to…
This work addresses the robust reconstruction problem of a sparse signal from compressed measurements. We propose a robust formulation for sparse reconstruction which employs the $\ell_1$-norm as the loss function for the residual error and…
We revisit the problem of robust principal component analysis with features acting as prior side information. To this aim, a novel, elegant, non-convex optimization approach is proposed to decompose a given observation matrix into a…
Compressed sensing deals with the recovery of sparse signals from linear measurements. Without any additional information, it is possible to recover an $s$-sparse signal using $m \gtrsim s \log(d/s)$ measurements in a robust and stable way.…
We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic…
In phase retrieval, the goal is to recover a complex signal from the magnitude of its linear measurements. While many well-known algorithms guarantee deterministic recovery of the unknown signal using i.i.d. random measurement matrices,…
Compressed sensing aims to undersample certain high-dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a…
Traditional sampling theories consider the problem of reconstructing an unknown signal $x$ from a series of samples. A prevalent assumption which often guarantees recovery from the given measurements is that $x$ lies in a known subspace.…
We propose a method to reconstruct sparse signals degraded by a nonlinear distortion and acquired at a limited sampling rate. Our method formulates the reconstruction problem as a nonconvex minimization of the sum of a data fitting term and…
We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover…
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…