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 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.