ACCELERATION OF LANDWEBER-TYPE ALGORITHMS BY SUPPRESSION OF PROJECTION ON THE MAXIMUM SINGULAR VECTOR

We develop a new procedure that speeds up convergence during the initial stage (the first 100 forward and backward projections) of Landweber-type algorithms, iterative image reconstruction for PET, which include the Landweber, generalized Landweber, and steepest descent algorithms. The procedure first identifies the singular vector associated with the maximum singular value of the PET system matrix, and then suppresses projection of the data on this singular vector after a single Landweber iteration. We show that typical PET system matrices have a significant gap between their two largest singular values; hence, this suppression allows larger gains in subsequent iterations, speeding up convergence by roughly a factor of three. New contributions of this paper include: 1) study of the singular value spectra of typical PET system matrices, 2) study of the effect on convergence of projection on the maximum singular vector, and 3) study of the convergence behavior of the new procedure applied to the Landweber, generalized Landweber, steepest descent, conjugate gradient, and ART algorithms (comparison is also made with the MLEM algorithm).