Maximum a posteriori estimation for SPECT using regularization techniques on massively parallel computers

Single photon emission computed tomography (SPECT) reconstructions performed using maximum a posteriori (penalized likelihood) estimation with the expectation maximization algorithm are discussed. Due to the large number of computations, the algorithms were performed on a massively parallel single-instruction multiple-data computer. Computation times for 200 iterations, using I.J. Good and R.A. Gaskins´s (1971) roughness as a rotationally invariant roughness penalty, are shown to be on the order of 5 min for a 64×64 image with 96 view angles on an AMT-DAP 4096 processor machine and 1 min on a MasPar 4096 processor machine. Computer simulations performed using parameters for the Siemens gamma camera and clinical brain scan parameters are presented to compare two regularization techniques-regularization by kernel sieves and penalized likelihood with Good´s rotationally invariant roughness measure-to filtered backprojection. Twenty-five independent sets of data are reconstructed for the pie and Hoffman brain phantoms. The average variance and average deviation are examined in various areas of the brain phantom. It is shown that while the geometry of the area examined greatly affects the observed results, in all cases the reconstructions using Good´s roughness give superior variance and bias results to the two alternative methods