Department of Mathematics, Francis Marion University, Florence, SC, USA.
School of Science Technology, American Public University System, Manassas, VA, USA.
J Xray Sci Technol. 2014;22(2):197-211. doi: 10.3233/XST-140419.
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.
在压缩感知框架中引入了块循环投影方法（BCPCS），用于计算机断层扫描中的图像重建，并且已经证明了在松弛参数为 1（λ=1）的情况下的收敛性。在本文中，我们证明了其在松弛参数 λ∈(0,1)的情况下的收敛性。因此，在一定条件下，推导出了具有松弛参数的基于压缩感知的块分量平均算法（BCAVCS）和块对角松弛正交投影算法（BDROPCS）的收敛性。通过选择的参数给出了实验来说明这些算法的收敛行为。
