NEW METHODS FOR FINDING VALUES OF THE JUMPS OF A FUNCTION FROM ITS LOCAL TOMOGRAPHIC DATAX

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 discontinuity 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 tomographic data, that is, from the knowledge of (f) over cap(theta, p) for theta, p in the region \theta . x(0) - p\ less than or equal to d, where d > 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.