On a method of image reconstruction of anisotropic media using applied quasipotential tomographic data

An algorithm for solving the coefficient problems of parameter identification of anisotropic media using applied quasipotential tomographic data is modified for the case of presence of more specific a priori information about the eigendirections of the corresponding conductivity tensor.  Its application is quite common in practice, in particular, in medicine, where the object of such study may be the medium with fibrous or layered areas (which includes muscles, bones, etc.), inside which there are streams of non-spherical particles (e.g. red blood cells).  As in our previous works, the corresponding algorithm is based on alternately solving the quasiconformal mapping and parameter identification problems, but in this work it is supplemented by the procedure of parallelization of calculations and the optimization problem is "accelerated".  The latter is characterized by a significant decrease in the number of intermediate calculations and, when imposing additional restrictions on eigendirections of the conductivity tensor, leads to the possibility of optimal adaptation of the algorithm to specific cases of practice.  The results of numerical experiments of imitative restoration of medium structure are presented.