MAXIMUM-LIKELIHOOD, LEAST-SQUARES, AND PENALIZED LEAST-SQUARES FOR PET

The EM algorithm is the basic approach used to maximize the log likelihood objective function for the reconstruction problem in PET. The EM algorithm is a scaled steepest ascent algorithm that elegantly handles the nonnegativity constraints of the problem. We show that the same scaled steepest descent algorithm can be applied to the least squares merit function, and that it can be accelerated using the conjugate gradient approach. Our experiments suggest that one can cut the computation by about a factor of 3 by using this technique. Our results also apply to various penalized least squares functions which might be used to produce a smoother image.