Acceleration of Landweber-type algorithms by suppression of projection on the maximum singular vector

A procedure that speeds up convergence during the initial stage (the first 100 forward and backward projections) of Landweber-type algorithms, for iterative image reconstruction for positron emission tomography (PET), which include the Landweber, generalized Landweber, and steepest descent algorithms, is discussed. 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. It is shown 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.