基于近似逐次超松弛预处理的自适应CQ算法

在处理基于不完全数据重建的不适定反问题时, 针对预处理CQ算法存在的不足, 提出了一种近似的逐次超松弛自适应预处理矩阵选择策略. 该方法利用近似特征值矩阵在处理矩阵相乘和求逆中的优势, 将正则化与超松弛预处理方法合, 通过迭代逐次逼近预处理矩阵, 并给出了算法的自适应步长. 结合稀疏角度CT图像重建问题, 给出了算具体实现步骤, 通过仿真可以验证: 该策略可以使预处理CQ算法有较快的收敛速度; 当存在噪声时,也可以较好地通过提前停止迭代来提高重建精度. 该策略为预处理CQ算法在不完全数据重建领域的应用提供了参考.

Approximate method for adaptive CQ algorithm based on successive over-relaxation preconditioning technology

As dealing with the ill-posed inverse problem, which based on the incomplete data reconstruction, and in order to improve the preconditioning CQ algorithm, an approximate method of defining adaptive preconditioning matrix is proposed. The matrix is constructed by the successive over-relaxation technology. Taking the advantages of the approximate eigenvalue matrix, the multiplication and inversion of matrixes could be easily implemented. The regularization was combined with over-relaxation preconditioned method. The preconditioning matrix could be approached successively through iterations, and an adaptive step-size could also be obtained. Considering the sparse angular CT image reconstruction problem, the implemented steps were presented, then the simulation results verified that the proposed method had faster convergence rate; to noised data, better reconstructed precision could be got by advance stopping iteration. The proposed method offers a reference for the application of preconditioning CQ algorithm on the field of incomplete data reconstruction.