Related papers: Low-Rank Toeplitz Matrix Estimation via Random Ult…
Finding a sparse representation of a possibly noisy signal can be modeled as a variational minimization with l_q-sparsity constraints for q less than one. Especially for real-time, on-line, or iterative applications, in which problems of…
Many popular statistical models, such as factor and random effects models, give arise a certain type of covariance structures that is a summation of low rank and sparse matrices. This paper introduces a penalized approximation framework to…
We study high-dimensional least-squares regression within a subgaussian statistical learning framework with heterogeneous noise. It includes $s$-sparse and $r$-low-rank least-squares regression when a fraction $\epsilon$ of the labels are…
This paper considers the use of total variation regularization in the recovery of approximately gradient sparse signals from their noisy discrete Fourier samples in the context of compressed sensing. It has been observed over the last…
In this paper, {the goal is to design deterministic sampling patterns on the sphere and the rotation group} and, thereby, construct sensing matrices for sparse recovery of band-limited functions. It is first shown that random sensing…
Suppose that we observe entries or, more generally, linear combinations of entries of an unknown $m\times T$-matrix $A$ corrupted by noise. We are particularly interested in the high-dimensional setting where the number $mT$ of unknown…
In this letter, we propose an algorithm for recovery of sparse and low rank components of matrices using an iterative method with adaptive thresholding. In each iteration, the low rank and sparse components are obtained using a thresholding…
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…
We consider tensor factorizations based on sparse measurements of the components of relatively high rank tensors. The measurements are designed in a way that the underlying graph of interactions is a random graph. The setup will be useful…
We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…
This article considers recovery of signals that are sparse or approximately sparse in terms of a (possibly) highly overcomplete and coherent tight frame from undersampled data corrupted with additive noise. We show that the properly…
We introduce an adaptive structured low rank algorithm to recover MR images from their undersampled Fourier coefficients. The image is modeled as a combination of a piecewise constant component and a piecewise linear component. The Fourier…
We present a new deterministic algorithm for the sparse Fourier transform problem, in which we seek to identify k << N significant Fourier coefficients from a signal of bandwidth N. Previous deterministic algorithms exhibit quadratic…
The alternating least squares algorithm for CP and Tucker decomposition is dominated in cost by the tensor contractions necessary to set up the quadratic optimization subproblems. We introduce a novel family of algorithms that uses…
Low-rank tensor recovery problems have been widely studied in many applications of signal processing and machine learning. Tucker decomposition is known as one of the most popular decompositions in the tensor framework. In recent years,…
This paper is concerned with specular reflection removal based on tensor low-rank decomposition framework with the help of polarization information. Our method is motivated by the observation that the specular highlight of an image is…
Matrix decompositions are fundamental tools in the area of applied mathematics, statistical computing, and machine learning. In particular, low-rank matrix decompositions are vital, and widely used for data analysis, dimensionality…
In this paper, we consider signals with a low-rank covariance matrix which reside in a low-dimensional subspace and can be written in terms of a finite (small) number of parameters. Although such signals do not necessarily have a sparse…
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…
In this paper, we construct a parameter estimation framework for robust low-rank tensor regression based on a truncation method and Huber loss, specifically focusing on models with random noise having only finite second-order moments.…