2142	 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. approximation biomedical image processing efficient encoding image processing linear programming mathematical programming Monte Carlo techniques optimization picture compression picture description picture processing stereology X-ray analysis
