Constrained Kaczmarz extended algorithm for image reconstruction

In this paper, we present a constrained version of Kaczmarz extended algorithm for improving image reconstruction from projections in computerized tomography. We prove convergence of our algorithm in the general inconsistent case to a “constrained” least squares solution of the reconstruction problem, under weaker hypothesis than those proposed in a previous paper by Koltracht and Lancaster for classical Kaczmarz’s projection method. Numerical experiments and comparisons are also presented on some model problems from the field of electromagnetic geotomography.