Column-relaxed algebraic reconstruction algorithm for tomography with noisy data

A tomographic reconstruction algorithm similar to the well-known algebraic reconstruction technique (ART) is presented. Similar to ART, the approximate algebraic reconstruction technique (AART) technique consists of a sequence of displacements of the image vector based on the projection error. AART is a column-relaxation technique that is a series of vector displacements of the image vector parallel to its coordinate axes. AART is compared with ART, a standard conjugate-gradient technique, and a conjugate-gradient technique augmented by nonnegativity. The use of relaxation parameters to improve the performance of both ART and AART in the presence of noise is discussed, and the use of an iteration termination criterion based on random generalized cross validation is illustrated.