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.