The convergence of the block cyclic projection with an overrelaxation parameter for compressed sensing based tomography

The convergence of the block cyclic projection for compressed sensing based tomography (BCPCS) algorithm had been proven recently in the case of underrelaxation parameter λ∈(0,1]. In this paper, we prove its convergence with overrelaxation parameter λ∈(1,2). As a result, the convergence of the other two algorithms (BCAVCS and BDROPCS) with overrelaxation parameter λ∈(1,2) in a special case is derived. Experiments are given to demonstrate the convergence behavior of the BCPCS algorithm with different values of λ.