Acceleration of kaczmarz using orthogonal subspace projections

Abstract

The Kaczmarz iterative algorithm is widely used to solve inconsistent over-determined linear systems, such as in computed tomography. This paper introduces an algorithm for improving convergence of Kaczmarz's method using projections into orthogonal subspaces from randomly selected measurement hyperplanes. In preliminary simulations, the method is computationally feasible, allows variable convergence acceleration with penalty-cost, but statistically reduces iterative errors. We evaluated our algorithm using simulations of uniform random Gaussian sampling on the unit sphere and the standard phantom image. The algorithm shows promise for inversions in diagnostic methods in biomedical applications and related problems in bioinformatics via parallel high-performance computing platforms.