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.

CACM December, 1971

Gordon,R.
Herman, G. T.

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

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CA711201 JB February 2, 1978  10:32 AM

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