Mathematical models and algorithms for reconstruction of singular support of functions and vector fields by tomographic data

E. Yu. Derevtsov, S. V. Mal'tseva, I. E. Svetov

Novosibirsk State University

Abstract: A problem of reconstruction of singularities of given in a unit disk scalar and vector fields is investigated. The Radon and ray transforms serves as initial date for the problem. Tools of mathematical modeling and numerical experiments are applied. Specially the task of visualization of lines of the fields and their derivatives breaks is considered. We propose the operators of indicators of inhomogeneity and breaks for the numerical solution to the problem. This indicators are constructed on a base of the differential operators and the integral operators of back-projection and angular moments. Suggested approaches serve as a basis for the algorithms which are realized numerically and investigated by simulation tests.

Keywords: tomography, Radon transform, ray transform, vector field, non-smooth function, singular support, back-projection operator, tensor analysis.

MSC: 44A12, 65R10, 65R32

Received: 25.11.2015

Language: English