New methods for finding values of the jumps of a function from its local tomographic data
- 1 October 1995
- journal article
- Published by IOP Publishing in Inverse Problems
- Vol. 11 (5) , 1005-1023
- https://doi.org/10.1088/0266-5611/11/5/005
Abstract
Let f( theta ,p) denote the Radon transform of f(x), x in R2, where f is a piecewise-smooth function with discontinuity curve S. Fix any x0 in S. The problem is to find the size of the jump of f across S at a point x0 from local tomographic data, that is, from the knowledge of f( theta ,p) for theta , p in the region mod theta .x0-p mod 0 is a given small number. Two groups of methods for solving this problem are proposed. One group is based on local tomography (LT) and on the investigation of the behaviour of the LT function in a neighbourhood of S. The second group is based on a new family of pseudolocal tomography (PLT) functions and the relation between LT and PLT functions, which is established in the paper. Results of testing the algorithms are presented.Keywords
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