On Signal Reconstruction in the Uniform Norm Taking into Account a priori Information in the Form of Differential Equations Describing Signal Forming

摘要

Passive thermoacoustic tomography is one of the most promising methods for the noninvasive determination of body inner temperature distribution, an urgent task of medical diagnostics. In this paper, the methods and algorithms for reconstructing the amplitude of a temperature distribution are examined. The functional is introduced whose minimization gives the best approximation of the source temperature distribution in the problem of thermoacoustic tomography. The algorithm for solving the problem of thermoacoustic tomography taking into account the heat equation is developed. The results of numerical simulation of reconstructing a temperature distribution by the proposed method are presented. These results are compared with those obtained by using the Tikhonov regularization method.