Generalized EM-Type Reconstruction Algorithms for Emission Tomography

We provide a general form for many reconstruction estimators of emission tomography. These estimators include Shepp and Vardi´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 others. We derive a generic update rule by constructing a surrogate function. This work is inspired by the ML-EM (EM, expectation maximization), where the latter naturally arises as a special case. A regularization with a specific form can also be incorporated by De Pierro´s trick. We provide a general and quite different convergence proof compared with the proofs of the ML-EM and De Pierro. Theoretical analysis shows that the proposed algorithm monotonically decreases the cost function and automatically meets nonnegativity constraints. We have introduced a mechanism to provide monotonic, self-constraining, and convergent algorithms, from which some interesting existing and new algorithms can be derived. Simulation results illustrate the behavior of these algorithms in term of image quality and resolution-noise tradeoff.