The convergence of block cyclic projection with underrelaxation parameters for compressed sensing based tomography.
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.
Department of Mathematics, Francis Marion University, Florence, SC, USA.
Fangjun
F
Arroyo
School of Science Technology, American Public University System, Manassas, VA, USA.
Edward
E
Arroyo
Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA, USA.
Xiezhang
X
Li
Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA, USA.
Jiehua
J
Zhu
D000465:Algorithms; D003198:Computer Simulation; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D019047:Phantoms, Imaging; D014057:Tomography, X-Ray Computed / Q000379:methods*
Compressed sensing; amalgamated projection method; block iterative algorithm; image reconstruction; total variation minimization