Noise revealing in Golub-Kahan bidiagonalization as a mean of regularization in discrete inverse problems

• ID: 2676, RIV: 10285035
• ISSN: not specified, ISBN: 978-80-87136-16-4
• source: SNA´14 - Seminar on Numerical Analysis: Modelling and Simulation of Challenging Engineering Problems
• keywords: ill-posed problems; regularization; Krylov subspace
• authors: Marie Kubínová, Iveta Hnětynková
• authors from KNM: Hnětynková Iveta

Abstract

We consider a linear inverse problem Ax ~ b, where A is a linear operator with smoothing property and b represents an observation vector polluted by unknown noise. It was shown that high-frequency noise reveals during the Golub-Kahan iterative bidiagonalization in the left bidiagonalization vectors. We present a method that identifies the iteration with maximal noise revealing and reduces a portion of high-frequency noise in the data by subtracting the corresponding (properly scaled) left bidiagonalization vector from b.