Deriving the multiplicative algebraic reconstruction algorithm (MART) by the method of convex projection (POCS)

TitleDeriving the multiplicative algebraic reconstruction algorithm (MART) by the method of convex projection (POCS)
Publication TypeConference Paper
Year of Publication1993
AuthorsMailloux, G. E., R. Noumeir, and R. Lemieux
Conference NameAcoustics, Speech, and Signal Processing, 1993. ICASSP-93., 1993 IEEE International Conference on
Pagination457 -460 vol.5
Date Publishedapr.
Keywordsconvergence, Entropy, entropy maximization, image reconstruction, initial solution, medical image processing, method of convex projection, multiplicative algebraic reconstruction algorithm, POCS, set theory, tomography
Abstract

It is shown that the MART (multiplicative algebraic reconstruction technique) algorithm can be derived by POCS. This gives MART a new theoretical interpretation and a proof of convergence to a stable solution even when other convex constraints are introduced. However, MART, as a multiplicative algorithm, depends on the initial solution. It is noted that, far from being a flaw, this property can be used to introduce further a priori knowledge about the image to be reconstructed, to maximize the entropy, to keep the ratio between the regions of the original image constant, or to set to zero the area outside the reconstruction volume. MART should be preferred to MENT (a maximum entropy algorithm) for entropy maximization, for it performs as well but is much faster. ART is much less influenced by the initial solution than MART

URLhttp://dx.doi.org/10.1109/ICASSP.1993.319846
DOI10.1109/ICASSP.1993.319846

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