Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460, USA.
J Xray Sci Technol. 2010;18(4):369-79. doi: 10.3233/XST-2010-0267.
The amalgamated projection method for convex feasibility and optimization problems has recently been proposed and the stable convergence under summable perturbations has been derived. As an application in computerized tomography (CT), the accuracy and the rate of convergence of the cyclic projection method and Cimmino algorithm incorporated with total variation minimization under certain conditions are significantly improved based on the theory of compressed sensing. In this paper, a varying block cyclic projection method and a block Cimmino's algorithm in the compressed sensing framework are proposed and their convergence are derived with an application of the convergence theorem of the amalgamated projection methods. An example is given to illustrate the convergence behavior of new algorithms.
最近提出了凸可行性和优化问题的合并投影方法，并推导出了可加扰动下的稳定收敛性。作为计算机断层扫描（CT）的应用，基于压缩感知理论，改进了循环投影法和共变最小化的 Cimmino 算法在某些条件下的准确性和收敛速度。本文提出了一种压缩感知框架下的变块循环投影法和块 Cimmino 算法，并利用合并投影方法的收敛定理推导出了它们的收敛性。给出了一个例子来说明新算法的收敛行为。
