Iterative relaxation methods for image reconstruction

The problem of recovering an image (a function of two variables) from experimentally available integrals of its grayness over thin strips is of great importance in a large number of scientific areas. An important version of the problem in medicine is that of obtaining the exact density distribution within the human body from X-ray projections. One approach that has been taken to solve this problem consists of translating the available information into a system of linear inequalities. The size and the sparsity of the resulting system of inequalities (typically, 25,000 inequalities with less than 1% of the coefficients nonzero) makes methods using successive relaxations computationally attractive. A variety of such methods have been proposed with differing relaxation parameters.