Singular Value Decomposition Approximation via Kronecker Summations for Imaging Applications
Numerical Analysis
2018-04-03 v2
Abstract
In this paper we propose an approach to approximate a truncated singular value decomposition of a large structured matrix. By first decomposing the matrix into a sum of Kronecker products, our approach can be used to approximate a large number of singular values and vectors more efficiently than other well known schemes, such as randomized matrix algorithms or iterative algorithms based on Golub-Kahan bidiagonalization. We provide theoretical results and numerical experiments to demonstrate the accuracy of our approximation and show how the approximation can be used to solve large scale ill-posed inverse problems, either as an approximate filtering method, or as a preconditioner to accelerate iterative algorithms.
Cite
@article{arxiv.1803.11525,
title = {Singular Value Decomposition Approximation via Kronecker Summations for Imaging Applications},
author = {Clarissa Garvey and Chang Meng and James G. Nagy},
journal= {arXiv preprint arXiv:1803.11525},
year = {2018}
}