Regularization parameter estimation for large-scale Tikhonov regularization using a priori information

• ID: 2515, RIV: 10051684
• ISSN: 0167-9473, ISBN: not specified
• source: Computational Statistics and Data Analysis
• keywords: Regularization; parameter; estimation; for; large-scale; Tikhonov; regularization; using; priori; informations
• authors: Rosemary Renaut, Iveta Hnětynková, Jodi Mead
• authors from KNM: Hnětynková Iveta

Abstract

This paper is concerned with estimating the solutions of numerically ill-posed least squares problems through Tikhonov regularizqation. Given apriori on the covariance structure of errors in the measurement data b, and a suiatble statistically-chosen regularization parameter, the Tikhonov regularized least squares functional J approximately follows a chi2 distribution with M degrees of freedom. Using the generalised singular value decomposition a regularization parameter can then be found such that resulting J follows this chi2 distribution, see Mead and Renaut (2008)