Golub-Kahan iterative bidiagonalization represents the core algorithm in regularization of large linear noise-polluted inverse problems. Regularization is here achieved via projection on a sequence of Krylov subspaces dominated by low-frequency vectors. Here we consider a general noise setting and analyze regularization effect of bidiagonalization-based methods LSQR, LSMR, and CRAIG, by relating their residuals with propagated noise. We discuss validity of our results in image deblurring problems. Influence of the loss of orthogonality is considered.

This presentation is part of Minisymposium “MS8 - Krylov Methods in Imaging: Inverse Problems, Data Assimilation, and Uncertainty Quantification (2 parts)”
organized by: Arvind Saibaba (North Carolina State University) , Julianne Chung (Virginia Tech) , Eric de Sturler (Virginia Tech) .

Authors:

Iveta Hnetynkova (Charles University, Faculty of Mathematics and Physics)

Keywords:

image deblurring, inverse problems, krylov subspaces, noise, numerical linear algebra, regularization