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Rapid advances during the past ten years of several forms of computer-assisted tomography (CT) have resulted in the development of numerous algorithms to convert raw projection data into cross-sectional images. These reconstruction algorithms are either "iterative," in which a large matrix algebraic equation is solved by successive approximation techniques; or "closed form." Continuing evolution of the closed form algorithms has allowed the newest versions to produce excellent reconstructed images in most applications. This paper will review several computer software and special-purpose digital hardware implementations of closed form algorithms, either proposed during the past several years by a number of workers or actually implemented in commercial or research CT scanners. The discussion will also cover a number of recently investigated algorithmic modifications which reduce the amount of computation required to execute the reconstruction process, as well as several new special-purpose digital hardware implementations under development in our laboratories at the Mayo Clinic.