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We introduce a general iterative scheme for image reconstruction based on Landweber's method. In our configuration, a sequential block-iterative (SeqBI) version can be readily formulated from a simultaneous block-iterative (SimBI) version, and vice versa. This provides a mechanism to derive new algorithms from known ones. It is shown that some widely used iterative algorithms, such as the algebraic reconstruction technique (ART), simultaneous ART (SART), Cimmino's, and the recently designeddoi:10.1109/tmi.2003.812253 pmid:12846426 fatcat:7zk7xqvwzfcyrprvspkud6xz6e