Reconstruction of pictures from their projections

There are situations in the natural sciences and medicine (e.g. in electron microscopy and X-ray photography) in which it is desirable to estimate the gray levels of a digital picture at the individual points from the sums of the gray levels along straight lines (projections) at a few angles. Usually, in such situations, the picture is far from determined and the problem is to find the “most representative” picture. Three algorithms are described (all using Monte Carlo methods) which were designed to solve this problem. The algorithms are applicable in a large and varied number of fields. The most important uses may be the reconstruction of possibly asymmetric particles from electron micrographs and three-dimensional X-ray analysis.