Related papers: Compression Approaches for the Regularized Solutio…
The high-order relations between the content in social media sharing platforms are frequently modeled by a hypergraph. Either hypergraph Laplacian matrix or the adjacency matrix is a big matrix. Randomized algorithms are used for low-rank…
This paper develops a general framework for solving a variety of convex cone problems that frequently arise in signal processing, machine learning, statistics, and other fields. The approach works as follows: first, determine a conic…
We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…
In this paper, we propose a low rank approximation method for efficiently solving stochastic partial differential equations. Specifically, our method utilizes a novel low rank approximation of the stiffness matrices, which can significantly…
We propose an algebraic combinatorial method for solving large sparse linear systems of equations locally - that is, a method which can compute single evaluations of the signal without computing the whole signal. The method scales only in…
This paper introduces a preconditioned method designed to comprehensively address the saddle point system with the aim of improving convergence efficiency. In the preprocessor construction phase, a technical approach for solving the…
How can we compute the pseudoinverse of a sparse feature matrix efficiently and accurately for solving optimization problems? A pseudoinverse is a generalization of a matrix inverse, which has been extensively utilized as a fundamental…
We introduce a new general purpose multiresolution preconditioner for symmetric linear systems. Most existing multiresolution preconditioners use some standard wavelet basis that relies on knowledge of the geometry of the underlying domain.…
We propose new algorithms for singular value decomposition (SVD) of very large-scale matrices based on a low-rank tensor approximation technique called the tensor train (TT) format. The proposed algorithms can compute several dominant…
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…
We consider the recovery of a low rank and jointly sparse matrix from under sampled measurements of its columns. This problem is highly relevant in the recovery of dynamic MRI data with high spatio-temporal resolution, where each column of…
Compressive sensing (CS) reconstructs images from sub-Nyquist measurements by solving a sparsity-regularized inverse problem. Traditional CS solvers use iterative optimizers with hand crafted sparsifiers, while early data-driven methods…
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 covariance matrix estimation, one of the challenges lies in finding a suitable model and an efficient estimation method. Two commonly used modelling approaches in the literature involve imposing linear restrictions on the covariance…
Low-order linear System IDentification (SysID) addresses the challenge of estimating the parameters of a linear dynamical system from finite samples of observations and control inputs with minimal state representation. Traditional…
When given a generalized matrix separation problem, which aims to recover a low rank matrix $L_0$ and a sparse matrix $S_0$ from $M_0=L_0+HS_0$, the work \cite{CW25} proposes a novel convex optimization problem whose objective function is…
In this paper we show how to recover a spectral approximations to broad classes of structured matrices using only a polylogarithmic number of adaptive linear measurements to either the matrix or its inverse. Leveraging this result we obtain…
Many problems can be formulated as recovering a low-rank tensor. Although an increasingly common task, tensor recovery remains a challenging problem because of the delicacy associated with the decomposition of higher order tensors. To…
This paper studies the problem of sampling vector and tensor signals, which is the process of choosing sites in vectors and tensors to place sensors for better recovery. A small core tensor and multiple factor matrices can be used to…
The theory of (tight) wavelet frames has been extensively studied in the past twenty years and they are currently widely used for image restoration and other image processing and analysis problems. The success of wavelet frame based models,…