Singular Value Decomposition Approximation via Kronecker Summations for Imaging Applications

Clarissa Garvey; Chang Meng; James G. Nagy

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arXiv · 1803.11525

Singular Value Decomposition Approximation via Kronecker Summations for Imaging Applications

Clarissa Garvey·Chang Meng·James G. Nagy

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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.

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BibTeX RIS

Clarissa Garvey, Chang Meng, James G. Nagy. 2018-03-30. Singular Value Decomposition Approximation via Kronecker Summations for Imaging Applications. https://arxiv.org/abs/1803.11525

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