FAST METHODS FOR INCLUDING ATTENUATION IN THE EM ALGORITHM

Attenuation of γ-rays within the body has for some time been recognized as one of the major factors affecting emission tomography data. The manner in which it is treated impacts on the accuracy of the reconstruction. An exact treatment of known or estimated attenuation can be formulated for least squares or maximum likelihood solutions by direct inclusion of the attenuation probabilities in the forward/back projections found in typical iterative algorithms. This approach has required ray tracing and summing of the attenuation coefficients along each ray path which is extremely computationally cumbersome. A fast approach to including attenuation in iterative maximum likelihood and least squares algorithms for SPECT is presented. Ray-tracing and summing of attenuation coefficients are replaced by the use of two look-up tables, one to compute attenuated ray path integrals based on a set of polar grid points and one to perform polar-to-rectangular transformations. The resulting algorithm implements a spatial average which is comparable in accuracy to ray-tracing with rectangular pixels yet requires less than one sixteenth the CPU time. Copyright © 1990 by The Institute of Electrical and Electronics Engineers, Inc.