NATURAL PIXEL DECOMPOSITION FOR TWO-DIMENSIONAL IMAGE RECONSTRUCTION.

In two-dimensional image reconstruction from line integrals using maximum likelihood, Bayesian, or minimum variance algorithms, the x-y plane on which the object estimate is defined is decomposed into nonoverlapping regions, or ″pixels″ . This decompostion of an otherwise continuous structure results in significant errors, or model noise, which can exceed the effects of the fundamental measurement noise. Many applications of diagnostic cross-sectional imaging require that images be obtained from limited data. A new formalism provides a connection between the continuous object to be reconstructed and its discrete representation. Using this formalism, the authors describe a decomposition of the x-y plane into a set of discrete, but overlapping pixels. In this model the pixels are uniquely defined by the beam paths. These ″natural″ pixels provide new, discrete filtered back projection reconstruction algorithms for limited data. The resulting reconstruction system not only avoids the pixel partitioning error, but provides basic mathematical properties which lead to profound computational advantages.