Numerical solvers based on the method of approximate inverse for 2D vector and 2-tensor tomography problems. (27th October 2017)

• Record Type: Journal Article
• Authors: Derevtsov, E Yu; Louis, A K; Maltseva, S V; Polyakova, A P; Svetov, I E
• Is Part Of: Inverse problems. Volume 33:Number 12(2017:Dec.)
• Publication Date: 2017-10-27
• Subjects: tensor tomography -- ray transform -- method of approximate inverse; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa8f5a
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: A problem of reconstruction of 2D vector or symmetric 2-tensor fields by their known ray transforms is considered. Two numerical approaches based on the method of approximate inverse are suggested for solving the problem. The first method allows to recover components of a vector or tensor field, and the second reconstructs its potentials in the sense of feature reconstruction, where the observation operator assigns to a field its potential. Numerical simulations show good results of reconstruction of the sought-for fields or their solenoidal or potential parts from its ray transforms.