Ai. Katsevich et Ag. Ramm, NEW METHODS FOR FINDING VALUES OF THE JUMPS OF A FUNCTION FROM ITS LOCAL TOMOGRAPHIC DATAX, Inverse problems, 11(5), 1995, pp. 1005-1023
Let (f) over cap(theta, p) denote the Radon transform of f(x), x is an
element of R(2), where f is a piecewise-smooth function with disconti
nuity curve S. Fix any x(0) is an element of S. The problem is to find
the size of the jump of f across S at a point x(0) from local tomogra
phic data, that is, from the knowledge of (f) over cap(theta, p) for t
heta, p in the region \theta . x(0) - p\ less than or equal to d, wher
e d > 0 is a given small number. Two groups of methods for solving thi
s problem are proposed. One group is based on local tomography (LT) an
d on the investigation of the behaviour of the LT function in a neighb
ourhood of S. The second group is based on a new family of pseudolocal
tomography (PLT) functions and the relation between LT and PLT functi
ons, which is established in the paper. Results of testing the algorit
hms are presented.