Solution of the inverse problem of restoring the signals from an electronic microscope in the backscattered electron mode on the class of bounded variation functions

Due to the fast evolution of micro- and nanotechnology, diagnostic techniques and research methods devoted to study micro objects are rapidly developed. One of such methods is the tomography in the backscattered electron mode. The spatial resolution of electronic microscope signals can be improved by solving the inverse problem of reconstructing a signal specified by the properties of the specimen under study and the electron probe in use. A method of solving this problem on the class of bounded total variation functions and its numerical implementation are considered. This work was partially supported by the Russian Foundation for Basic Research (project no. 11-01-00040) and a partial support by Visby Program, Swedish Institute, Stockholm.