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An incoherent low-rank matrix can be efficiently reconstructed after observing a few of its entries at random, and then solving a convex program that minimizes the nuclear norm. In many applications, in addition to these entries,…
The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…
The paper deals with the problem of finding sparse solutions to systems of polynomial equations possibly perturbed by noise. In particular, we show how these solutions can be recovered from group-sparse solutions of a derived system of…
In this paper, we study the problem of recovering a low-rank matrix (the principal components) from a high-dimensional data matrix despite both small entry-wise noise and gross sparse errors. Recently, it has been shown that a convex…
In this letter, we study the deterministic sampling patterns for the completion of low rank matrix, when corrupted with a sparse noise, also known as robust matrix completion. We extend the recent results on the deterministic sampling…
Linear sketching and recovery of sparse vectors with randomly constructed sparse matrices has numerous applications in several areas, including compressive sensing, data stream computing, graph sketching, and combinatorial group testing.…
Conventional sparse phase retrieval schemes can recover sparse signals from the magnitude of linear measurements only up to a global phase ambiguity. This work proposes a novel approach that instead utilizes the magnitude of affine…
Recovery of arbitrarily positioned samples that are missing in sparse signals recently attracted significant research interest. Sparse signals with heavily corrupted arbitrary positioned samples could be analyzed in the same way as…
This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions,…
We study how well one can recover sparse principal components of a data matrix using a sketch formed from a few of its elements. We show that for a wide class of optimization problems, if the sketch is close (in the spectral norm) to the…
We propose dimension reduction methods for sparse, high-dimensional multivariate response regression models. Both the number of responses and that of the predictors may exceed the sample size. Sometimes viewed as complementary, predictor…
Recovery of low-rank matrices has recently seen significant activity in many areas of science and engineering, motivated by recent theoretical results for exact reconstruction guarantees and interesting practical applications. A number of…
We consider the problem of recovering an $n_1 \times n_2$ low-rank matrix with $k$-sparse singular vectors from a small number of linear measurements (sketch). We propose a sketching scheme and an algorithm that can recover the singular…
Recovering jointly sparse signals in the multiple measurement vectors (MMV) setting is a fundamental problem in machine learning, but traditional methods often require careful parameter tuning or prior knowledge of the sparsity of the…
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.…
This paper studies the problem of recovering a signal vector and the corrupted noise vector from a collection of corrupted linear measurements through the solution of a l1 minimization, where the sensing matrix is a partial Fourier matrix…
This paper develops new methods to recover the missing entries of a high-rank or even full-rank matrix when the intrinsic dimension of the data is low compared to the ambient dimension. Specifically, we assume that the columns of a matrix…
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…
Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…
We study the problem of recovery of matrices that are simultaneously low rank and row and/or column sparse. Such matrices appear in recent applications in cognitive neuroscience, imaging, computer vision, macroeconomics, and genetics. We…