MAXIMUM-LIKELIHOOD SPECT IN CLINICAL COMPUTATION TIMES USING MESH-CONNECTED PARALLEL COMPUTERS

Extending our previous work in positron emission tomography [1], [2] this paper demonstrates that a fully parallel implementation of the maximum-likelihood method for single-photon emission computed tomography can be accomplished in clinical time frames on massively parallel systolic array processors. The implementation incorporates the depth-dependent point spread function and nonuniform attenuation correction required for the iterative solution of the ML estimation algorithm [3], [4] by mapping these components to a systolic array as follows. The measurement error kernel, linear along the line of flight and Gaussian parallel to the detector surface, is obtained via the heat equation as in PET [1], [2], with the depth dependences accommodated by successively convolving the image as the results propagate across the mesh array towards the detector surface. Nonuniform attenuation is obtained by storing the attenuation coefficient map in the array of processors, and differentially attenuating the data as it is propagated across the array. Variation with projection angle is accommodated by rotating the image grid using a parallel rotation technique based on defining "near circular" trajectories around the processor array, with processors locally passing their data store to their neighbors defined by the trajectories. These parallel methods are demonstrated on the distributed array processor of Active Memory Technocology, running at 1.5 s/iteration of the expectation maximization algorithm for image reconstructions of size 64 x 64 and data sets consisting of 96 view angles. These reconstruction times also include regularization using Good's rotationally invariant roughness prior, and demonstrate that Bayesian methods can be used for clinical image reconstructions in single-photon tomography in times which are on the order of 1 min/slice.