A numerical solution of the dynamic vector tomography problem using the truncated singular value decomposition method

Abstract

We consider a problem of dynamic 2D vector tomography, i.e. the object under investigation changes during the data acquisition. More precisely, we consider the case when the object motion is a combination of rotation and shifting. The task is then to reconstruct the searched-for vector field by known values of the dynamic ray transforms. In order to solve this dynamic inverse problem, we first study properties of the dynamic ray transforms operators. In particular, the singular value decompositions of the operators are constructed using classic orthogonal polynomials. Following from this study, a numerical algorithm for solving the dynamic problem is proposed based on the truncated singular value decomposition method.

Singular value decomposition for longitudinal, transverse and mixed ray transforms of 2D tensor fields

“…In [8,47] algorithms based on the truncated SVdecomposition method were developed and numerically implemented for the approximate recovery of two-dimensional vector and symmetric two-tensor fields. In addition, the SVdecomposition method was used to recover vector [32,34] and tensor [33] fields in the dynamic case.…”