Affiliations: Department of Mathematics, Francis Marion University,
Florence, SC, USA | School of Science Technology, American Public
University System, Manassas, VA, USA | Department of Mathematical Sciences, Georgia Southern
University, Statesboro, GA, USA
Note: [] Corresponding author: Fangjun Arroyo, Department of Mathematics,
Francis Marion University, Florence, SC 29501, USA. Tel.: +1 843 661 1594;
E-mail: farroyo@fmarion.edu
Abstract: The block cyclic projection method in the compressed sensing
framework (BCPCS) was introduced for image reconstruction in computed
tomography and its convergence had been proven in the case of unity relaxation
(λ=1). In this paper, we prove its convergence with
underrelaxation parameters λ∈(0,1). As a result, the
convergence of compressed sensing based block component averaging algorithm
(BCAVCS) and block diagonally-relaxed orthogonal projection algorithm (BDROPCS)
with underrelaxation parameters under a certain condition are derived.
Experiments are given to illustrate the convergence behavior of these
algorithms with selected parameters.
