Switching components and the ambiguity problem in the reconstruction of pictures from their projections

摘要

The information in a digital picture may be compressed by summing gray levels over known paths, or rays, of the picture. A projection is an ordered set of ray sums. Sets of projections may be used to store pictures in compressed form. Given a projection set, reconstruction is achieved by operating on the projection set to produce either the original picture or an approximation to it (called a similar picture). The latter is due to the ambiguity of the reconstruction technique inherent in the data compression.This paper describes the ambiguity problem resulting in picture reconstruction from projection sets. The concept of switching components, a key factor in the ambiguity, is discussed. Switching components are groups of picture points which can be changed in a certain way (therefore changing the original picture to a “similar” picture) without affecting the projection set.A technique is developed that addresses itself first to unambiguous areas of the picture in reconstruction. This technique is used along with more traditional methods for the doubtful areas.