Block‐iterative algorithms

Abstract The recently presented sequential unconstrained minimization algorithm, SUMMA, is extended to provide a framework for the derivation of block‐iterative, or partial‐gradient, optimization methods. This block‐iterative SUMMA (BI‐SUMMA) includes, and is motivated by, block‐iterative versions of the algebraic reconstruction technique (ART) and its multiplicative variant, the MART. The BI‐SUMMA approach is designed to provide computationally tractable and quickly convergent algorithms. The rescaled block‐iterative expectation maximization maximum likelihood method (RBI‐EMML) is closely related to the RBI‐MART, but is not a particular case of BI‐SUMMA.