基于Mumford-Shah正则项与L^1数据拟合的PET图像重建方法

PET Image Reconstruction Using Mumford-Shah Regularization Coupled with L^1 Data Fitting

在正电子发射断层重建(PET)算法中,正则项常被用来抑制噪声。本文将Mumford-Shah(MS)正则项与最新的L1数据保真项相结合,构造出一种新的变分结构用以进行PET图像重建。为了简化计算,本文采用了Ambrosio和Tortorelli提出的Г-收敛逼近方法,将MS函式对边界积分转化为一类合适的辅助光滑函数的区域积分。在仿真测试中,将算法与传统滤波反投影(FBP)算法,最大似然法(EM),最小交叉熵法(MXE)作比较。通过实验结果的研究,对算法的效率和可行性进行了分析。

In positron emission tomography （PET） image reconstruction, regularization methods are usually considered to suppress noise effects in reconstructed images. In this paper, we model this reconstruction problem in a new variational framework where the Mumford-Shah （MS） regularization coupled with recently developed L^1 data fidelity term is adapted. In order to simplify the numerical computation, Ambrosio and Tortorelli＇ s Г-convergence approximation is also employed to substitute the irregular parts （ edge set） of MS functionals with the auxiliary smooth function. In numerical studies we compare our method with FBP, EM as well as MXE algorithm. Results show both feasibility and efficiency of the proposed algorithm.