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

摘要

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.