A fast convergent ordered subset Bayesian reconstruction for emission tomography

Previously, we proposed an algorithm, ECOSEM-ML (Enhanced Complete-Data Ordered Subsets Expectation-Maximization), for fast maximum likelihood (ML) reconstruction in emission tomography (ET). Here we extend the ECOSEM algorithm to an maximum a posteriori (MAP) reconstruction by including a smoothing separable surrogate prior, and this new MAP algorithm is called ECOSEM-MAP. The ECOSEM-MAP reconstruction is founded on an incremental EM approach and one can show that the ECOSEM-MAP converges to the MAP solution. Other related MAP algorithms, including BSREM and OS-SPS algorithms, are fast and convergent, but require a judicious choice of a user-specified relaxation schedule. ECOSEM-MAP itself uses a sequence of iteration-dependent parameters (very roughly similar to relaxation parameters) to control a tradeoff between a greedy, fast but non-convergent update and a slower but convergent update. These parameters, however, are computed automatically at each iteration and require no user specification. Our simulations show that ECOSEM-MAP is nearly as fast as BSREM.