E. Yu. Derevtsov
An approach to direct reconstruction of a solenoidal part in vector and tensor tomography problems
The problem of reconstruction of vector and 2-tensor fields, given in refracting medium, is considered. The approach of direct reconstruction of a solenoidal part is presented. Least squares method is exploited for a reconstruction of solenoidal parts of original vector and 2-tensor fields by usage of certain solenoidal bases of polynomial type constructed for this purpose. The approach is justified theoretically by consideration of polynomial decompositions of polynomial vector and 2-tensor fields. The problems of existence, uniqueness and convergence of obtained approximation to the solenoidal part of original field are solved. The results of numerical simulation are presented and discussed.
Journal of Inverse and Ill-posed Problems, Walter de Gruyter
Print ISSN: 0928-0219
Volume: 13, 05/2005
Pages: 213 - 246
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