Block-iterative algorithms with underrelaxed Bregman projections

The notion of relaxation is well understood for orthogonal projec tions onto convex sets For general Bregman projections it was consid ered only for hyperplanes and the question of how to relax Bregman projections onto convex sets that are not linear ie not hyperplanes or halfspaces has remained open A denition of underrelaxation of Bregman projections onto general convex sets is given here which includes as special cases the underrelaxed orthogonal projections and the underrelaxed Bregman projections onto linear sets as given by De Pierro and Iusem With this new denition we construct a block iterative projection algorithmic scheme and prove its convergence to a solution of the convex feasibility problem The practical importance of relaxation parameters in the application of such projection algo rithms to realworld problems is demonstrated on a problem of image reconstruction from projections Key Words convex feasibility projection algorithms Bregman functions blockiterative algorithms underrelaxatio