稀疏角度CT图像重建的Huber-TV正则化方法  

Method of Huber-TV regularization for sparse angular CT image reconstruction

作　　者：李维 张本鑫 LI Wei;ZHANG Benxin(School of Electronic Engineering and Automation,Guilin University of Electronic Technology,Guilin 541004,China;Guangxi Key Laboratory of Automatic Detecting Technology and Instrument,Guilin 541004,China)

机构地区：[1]桂林电子科技大学电子工程与自动化学院,广西桂林541004 [2]广西自动检测技术与仪器重点实验室,广西桂林541004

出　　处：《现代电子技术》2023年第2期65-69,共5页Modern Electronics Technique

基　　金：国家自然科学基金资助项目(11901137);国家自然科学基金资助项目(61967004);广西自动检测技术与仪器重点实验室项目(YQ22108);桂林电子科技大学研究生教育创新计划项目(2022YCXS161)。

摘　　要：对于稀疏角度下的投影数据,计算机断层扫描重建图像容易出现分辨率低、伪影较多的问题,难以满足工业及医学诊断要求。文中从迭代重建的角度出发,提出一个结合全变分(TV)和Huber函数(Huber-TV)的CT重建方法。该方法利用Huber函数替代传统全变分模型中的L1范数,在合理控制函数阈值的条件下,充分利用Huber函数的线性部分对大于阈值的梯度图像进行较轻的惩罚,以保持图像边缘连续性;再结合二次项对小于阈值的梯度图像进行较大的惩罚,以抑制图像中不连续梯度跳跃。新模型目标函数的光滑性可以使得梯度下降法快速收敛到最优值,避开传统全变分模型中的次梯度计算,从而降低计算复杂度并加快迭代速度。实验结果表明,在稀疏角度重建条件下,与传统TV模型相比,Huber-TV模型的均方根误差降低19%,信噪比提升22.33 dB,说明所提方法高效可行。For projection data in sparse angles,the CT(computed tomography)reconstructed images are prone to the low resolution and many artifacts, which are difficult to meet the requirements of industry and medical diagnosis. From the perspective of iterative reconstruction,a CT reconstruction method combining total variation(TV) and Huber function is proposed. In this method,the Huber function is used to replace the L1 norm in the traditional total variation model. Under the condition of reasonable control of the function threshold,the linear part of the Huber function is fully utilized to slightly penalize the gradient image larger than the threshold to maintain the continuity of the image edge. In combination with the quadratic term,the gradient image smaller than the threshold value is penalized severely to suppress discontinuous gradient jump in the image. The smoothness of the objective function of the new model can make the gradient descent converge to the optimal value quickly,avoiding the subgradient calculation in the traditional TV model,thus reducing the computational complexity and accelerating the iteration speed. The experimental results show that,in comparison with the traditional TV model,the root mean square error of the Huber-TV model is reduced by 19%,and the signal-to-noise ratio is improved by 22.33 dB under the condition of sparse angular reconstruction,which verifies that the proposed method is efficient and feasible.

关 键 词：CT图像重建 梯度图像 全变分模型 Huber-TV 图像处理 数据分析 

分 类 号：TN911.73-34[电子电信—通信与信息系统]