Piecewise uniform regularization for the inverse problem of microtomography with a-posteriori error estimate

Abstract

ABSTRACTAn inverse microtomography problem is under consideration in a class of functions with bounded V H variation. An algorithm for solving this problem is proposed based on Tikhonov's regularization with a special regularizer. The algorithm ensures piecewise uniform convergence of approximate solutions to exact solution of the inverse problem. In addition, the question of a-posteriori error estimate of approximate solutions obtained is considered. A new numerical algorithm for finding this estimate is proposed. Numerical experiments on solving a model inverse problem on the class of functions with bounded V H variation are presented along with the results of a-posteriori error estimate for approximate solutions obtained.