基于变指数各向异性扩散和非局部的最大似然期望最大低剂量CT重建算法

MLEM low-dose CT reconstruction algorithm based on variable exponent anisotropic diffusion and non-locality

针对低剂量计算机断层扫描(CT)重建图像发生严重衰退的问题,提出一种基于变指数和非局部的最大似然期望最大(MLEM)低剂量CT重建算法。该算法考虑了传统各向异性扩散中降噪不充分的缺点,把可以有效折中热传导和各向异性扩散(P-M)这两种模型的变指数,以及代替梯度检测边缘和细节的相似度函数运用到传统各向异性扩散中,从而达到所期望的效果。该算法在每次迭代中首先采用基本的MLEM算法对低剂量CT投影数据进行重建;然后利用基于非局部的相似性测度以及变指数和模糊数学的理论对各向异性扩散的扩散函数进行改进,用改进后的各向异性扩散对重建图像进行降噪;最后使用中值滤波对图像进行处理从而消除脉冲噪声点。实验结果表明,所提出算法的均方绝对误差、归一化均方距离均比有序子集惩罚最小二乘(OS-PLS)、有序子集惩罚最大似然一步迟疑(OS-PML-OSL)、基于传统P-M、基于方差的算法小,获得了高达10.52的信噪比。该算法重建出的图像可以在有效消除噪声的同时较好地保持图像的边缘和细节信息。

Concerning the serious recession problems of the low-dose Computed Tomography （CT） reconstruction images, a low-dose CT reconstruction method of MLEM based on non-locality and variable exponent was presented. Considering the traditional anisotropic diffusion noise reduction is insufficient, variable exponent which could effectively compromise between heat conduction and anisotropic diffusion P-M models, and the similarity function which could detect the edge and details instead of gradient were applied to the traditional anisotropic diffusion, so as to achieve the desired effect. In each iteration, firstly, the basic MLEM algorithm was used to reconstruct the low-dose projection data. And then the diffusion function was improved by the non-local similarity measure, variable index and fuzzy mathematics theory, and the improved anisotropic diffusion was used to denoise the reconstructed image. Finally median filter was used to eliminate impulse noise points in the image. The experimental results show the proposed algorithm has a smaller numerical value than OS-PLS （ Ordered Subsets- Penalized Least Squares）, OS-PML-OSL （Ordered Subsets-Penalized Maximum Likelihood-One Step Late）, and the algorithm based on the traditional PM, in the variance of Mean Absolute Error （MAE）, and Normalized Mean Square Distance （NMSD）, especially its Signal-to-Noise Ratio （SNR） is up to 10.52. This algorithm can effectively eliminate the bar of artifacts, and can keep image edges and details information better.