相关论文: A Randomized Multivariate Matrix Pencil Method for…

Exponential is a basic signal form, and how to fast acquire this signal is one of the fundamental problems and frontiers in signal processing. To achieve this goal, partial data may be acquired but result in the severe artifacts in its…

This paper presents a new Bayesian collaborative sparse regression method for linear unmixing of hyperspectral images. Our contribution is twofold; first, we propose a new Bayesian model for structured sparse regression in which the…

Magnetic Particle Imaging (MPI) is a preclinical imaging technique capable of visualizing the spatio-temporal distribution of magnetic nanoparticles. The image reconstruction of this fast and dynamic process relies on efficiently solving an…

In the field of data mining, how to deal with high-dimensional data is an inevitable problem. Unsupervised feature selection has attracted more and more attention because it does not rely on labels. The performance of spectral-based…

In recent years, randomized methods for numerical linear algebra have received growing interest as a general approach to large-scale problems. Typically, the essential ingredient of these methods is some form of randomized dimension…

Image reconstruction in X-ray tomography is an ill-posed inverse problem, particularly with limited available data. Regularization is thus essential, but its effectiveness hinges on the choice of a regularization parameter that balances…

A sparse modeling approach is proposed for analyzing scanning tunneling microscopy topography data, which contains numerous peaks corresponding to surface atoms. The method, based on the relevance vector machine with $\mathrm{L}_1$…

Supervised classification and representation learning are two widely used classes of methods to analyze multivariate images. Although complementary, these methods have been scarcely considered jointly in a hierarchical modeling. In this…

Several recent methods used to analyze asymptotic stability of delay-differential equations (DDEs) involve determining the eigenvalues of a matrix, a matrix pencil or a matrix polynomial constructed by Kronecker products. Despite some…

X-ray Ptychography is an advanced computational microscopy technique which is delivering exceptionally detailed quantitative imaging of biological and nanotechnology specimens. However coarse parametrisation in propagation distance,…

The numerical solution of the generalized eigenvalue problem for a singular matrix pencil is challenging due to the discontinuity of its eigenvalues. Classically, such problems are addressed by first extracting the regular part through the…

We consider the distance from a (square or rectangular) matrix pencil to the nearest matrix pencil in 2-norm that has a set of specified eigenvalues. We derive a singular value optimization characterization for this problem and illustrate…

Binary deterministic sensing matrices are highly desirable for sampling sparse signals, as they require only a small number of sum-operations to generate the measurement vector. Furthermore, sparse sensing matrices enable the use of…

This note gives a simple analysis of a randomized approximation scheme for matrix multiplication proposed by Sarlos (2006) based on a random rotation followed by uniform column sampling. The result follows from a matrix version of…

Matrix completion is a widely used technique for image inpainting and personalized recommender system, etc. In this work, we focus on accelerating the matrix completion using faster randomized singular value decomposition (rSVD). Firstly,…

We introduce an eigenvalue-preserving transformation algorithm from the generalized eigenvalue problem by matrix pencil of the upper and the lower bidiagonal matrices into a standard eigenvalue problem while preserving sparsity, using the…

We present and analyze a novel sparse polynomial technique for the simultaneous approximation of parameterized partial differential equations (PDEs) with deterministic and stochastic inputs. Our approach treats the numerical solution as a…

In many problems in Computational Physics and Chemistry, one finds a special kind of sparse matrices, termed "banded matrices". These matrices, which are defined as having non-zero entries only within a given distance from the main…

Rigorous, non-asymptotic bounds for the Puiseux expansion of the eigenvalue at infinity are given. Error analysis is provided. Further, the expected value of the eigenvector condition number of a randomly perturbed matrix is estimated. The…

The distribution of the eigenvalues of a Hermitian matrix (or of a Hermitian matrix pencil) reveals important features of the underlying problem, whether a Hamiltonian system in physics, or a social network in behavioral sciences. However,…