具有约束的稀疏正则图像重建模型及其在CT成像中的应用

摘要

提出更具有一般性的约束稀疏正则图像重建模型,它不仅包含了各向异性和各向同性TV范数重建模型,而且可以推广到其他CT重建模型.基于Chambolle和Pock的原始对偶方法思想,借助指示函数,将原模型转化为无约束的凸优化模型,建立求解所得到优化模型的迭代算法,该算法的特点是无需内迭代以及计算矩阵逆且迭代每一步都具有显示解.进而,提出了一种自适应的原始对偶算法,将算法中固定迭代参数推广到可变参数情形.最后,将所提模型和算法应用于不完备投影CT重建问题,并与ART-POCS方法进行比较,得出我们的方法在图像重建质量等方面优于ART-POCS方法.%Amore general constrained sparse regularization image reconstruction model was proposed in this study,which not only contained the anisotropic and isotropic TV norm reconstruction model,but also can be extend-ed to other CT reconstruction model.Based on the Chambolle and Pock primal-dual method,the indicator function was used to transform the original model into an unconstrained convex optimization model,and an iterative algorithm was establish to solve the optimization model.The inner iteration and inverse of matrix was not involved in the algo-rithm doesn't involve.In particular,each iteration step has an explicit solution.Furthermore,an adaptive primal-dual algorithm was also proposed,where the iterative parameters were updated automatically.Finally,the proposed model and algorithm were applied to the problem of incomplete projection CT reconstruction and compared it with ART-POCS method.It was concluded that our method was superior to ART-POCS in terms of image reconstruction qual-ity.