ITERATIVE CHOICES OF REGULARIZATION PARAMETERS IN LINEAR INVERSE PROBLEMS

We investigate possibilities of choosing reasonable regularization par ameters for the output least squares formulation of linear inverse pro blems. Based on the Morozov and damped Morozov discrepancy principles, we propose two iterative methods, a quasi-Newton method and a two-par ameter model function method, for finding some reasonable regularizati on parameters in an efficient manner. These discrepancy principles req uire knowledge of the error level in the data of the considered invers e problems, which is often inaccessible or very expensive to achieve i n real applications. We therefore propose an iterative algorithm to es timate the observation errors for linear inverse problems. Numerical e xperiments for one- and two-dimensional elliptic boundary value proble ms and an integral equation are presented to illustrate the efficiency of the proposed algorithms.