Generalized EM-type Reconstruction Algorithms for

We provide a general form of many reconstruction estimators for emission tomography, which cover Shepp and Var- di's maximum likelihood (ML) estimator, the quadratic weighted least squares (WLS) estimator, Anderson's WLS estimator, and Liu and Wang's multi-objective estimator, and so on. We derive a generic update rule by a well-known method constructing a surrogate function. The work is inspired by the ML-EM (EM, expectation maximization), where the latter naturally arises as a special case. A regularization with specific form can also be incorporated using De Pierro's trick. We provide a general and quite different convergence proof compared with the proofs of the ML-EM and De Pierro. Theoretic analysis shows that the proposed algorithm monotonically decreases the cost function and automatically meets the nonnegativity constraints. We have introduced a mechanism to provide monotonic, self-constraining, and convergent algorithms, by which some interesting existing and new algorithms can be derived. Simulation results illustrate the behavior of these algorithms in image quality and resolution- noise tradeoff, etc. Index Terms—Global convergence, Kuhn-Tucker (KT) condi- tions, regularization technique, surrogate function.