Regularization parameter estimation for large-scale Tikhonov regularization using a priori information
2010
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)