紧框架小波和总广义全变分联合约束的医学图像复原算法  

Medical Image Restoration Algorithm Constrained by Both Tight Frame Wavelet and Total Generalized Variation

作　　者：张晶[1] 马瑾[1] 邵晨 桂志国[3] 张权[3] 杨婕 ZHANG Jing;MA Jin;SHAO Chen;GUI Zhi-guo;ZHANG Quana;YANG Jie(Dept. of Information Engineering, Shanxi Vocational ＆ Technical College of Finance ＆ Trade, Taiyuan 030031, China;School of Medicine Management, Shanxi University of Chinese Medicine, Taiyuan 030619, China;School of Information and Communication Engineering, North University of China, Taiyuan 030051, China)

机构地区：[1]山西财贸职业技术学院信息工程系,山西太原030031 [2]山西中医药大学医药管理学院,山西太原030619 [3]中北大学信息与通讯工程学院,山西太原030051

出　　处：《中北大学学报（自然科学版）》2017年第6期666-673,共8页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(61671413);国家重大科学仪器设备开发专项基金资助项目(2014YQ240445);爆炸科学与技术国家重点实验室基金资助项目(KFJJ13-11M);山西省自然科学基金资助项目(2015011046);电子测试技术重点实验室开放基金资助项目(ZDSYSJ2015006)

摘　　要：为了克服传统全变分正则化方法容易造成复原图像中出现阶梯状伪边缘、纹理细节丢失的不足,本文提出了一种紧框架小波和总广义全变分联合约束的图像复原算法.首先,结合紧框架小波能够捕获含噪声或退化图像中的奇异点的优势,同时采用能够逼近任意阶多项式函数进而可以保留图像尖锐边缘的总广义全变分,构造出一种由紧框架小波的L_1范数和二阶总广义全变分的L_2范数组成的联合正则项约束的图像复原模型;其次,采用交替方向迭代方法将所提模型的最小化问题分解为两个子问题,并分别采用均值增广拉格朗日算法和Chambolle-Pock一阶原始—对偶迭代方法获得最优解.实验结果表明,所提算法在抑制噪声的同时能够有效复原图像的边缘、细节信息,两种量化指标峰值信噪比和结构相似度的值也能直观体现复原图像质量的提高水平.In order to overcome the shortcomings of the traditional total variational regularization method, which easily caused the stair-stepping pseudo edges and texture details missing in the restored image, a tight frame wavelet and total generalized variation joint constrained image restoration algorithm were proposed in this paper. Firstly, considering the advantages of the tight frame wavelet in capturing singularities from noisy and degraded images, and by adopting the total generalized variation （TGV） which could maintain sharp edges through approximating any order polynomial function, a joint regulatory constraints which was composed of the norm of the tight frame wavelet and the L2 norm of TGV constrained image restoration model was constructed; secondly, by utilizing the alternating direction iteration method, the minimization problem of model was divided into two sub-problems. And the optimal solutions were respectively obtained by the mean doubly augmented Lagrangian （MDAL） and the Cham- bolle-Pock first-order primal-dual iterative method. Finally, the experimental results show that the proposed algorithm can effectively restore the edges and details while suppressing the noise, and the values of the two quantitative indicators namely peak signal-to-noise ratio （PSNR） and root mean squared error （RMSE） can also directly reflect the improvement of the restored image quality.

关 键 词：紧框架小波 总广义全变分 增广拉格朗日法 一阶原始—对偶迭代方法 医学图像复原算法 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]