基于Split-Bregman方法的稀疏角度CT重建算法研究

Study on Split- Bregman algorithm for sparse-view CT reconstruction

离散梯度变换已被广泛地用作稀疏算子,相应的全变差(TV)最小化方法也被用于基于压缩感知(CS)的CT重建中.与此同时Split-Bregman算法在求解L1正则化问题方面引起了很大关注,此方法对原来的L1正则化问题引入一个分裂变量后利用Bregman迭代求解.本文将Split-Bregman方法用于稀疏角度CT重建,并与传统的SART和基于SART的软阈值算法(STF-SART)进行比较,最后用Head模型作为测试模型进行仿真实验,实验结果表明:对于稀疏角度CT重建问题,TV正则化(STF-SART和Split-Bregman)算法明显优于传统的SART算法,且Split-Bregman算法在收敛速度和重建图像质量方面又优于STF-SART算法.

The TV minimize technique which corresponds to Discrete Gradient transform is widely used in the CT reconstruction basing on CS, including sparse -view reconstruction based on compressed sensing (CS).Meanwhile, Split-Bregman algorithm has caused great concern in solving L1 regularization issues , this method first introduces a split variation to the original regularized problem and then use Bregman iterative solve it .In this paper , we apply the Split -Bregman approach to reconstruct an ROI for the CS -based sparse -view CT reconstruction , and combined with the traditional SART algorithms and soft thresholding algorithm based on SART ( STF-SART ) . Finally Head model is applied as a test model to the simulation experiment ,and the results shows that:for sparse-view CT reconstruction , TV regularization ( STF-SART and Split-Bregman) algorithms outperform conventional SART algorithm, and Split-Bregman algorithm is superior to STF -SART algorithmsn terms of convergence speed and reconstructed image quality .