自适应非张量积小波紧框架图像去噪  

SELF-ADAPTIVE NON-TENSOR PRODUCT TIGHT WAVELET FRAME IMAGE DENOISING

作　　者：黄素莹 羿旭明[1] HUANG Su-ying;YI Xu-ming(School of Mathematics and Statistics,Wuhan University,Wuhan 430072,Chin)

机构地区：[1]武汉大学数学与统计学院,湖北武汉430072

出　　处：《数学杂志》2018年第3期549-556,共8页Journal of Mathematics

基　　金：国家自然科学基金面上项目(11671307)

摘　　要：本文研究了图像去噪的问题.利用光滑余因子协调法,构造了样条空间S_6~4(?_(mn)^(2))中的二元六次样条函数,以此作为尺度函数,并基于酉延拓定理,构造了非张量积小波紧框架.利用构造的非张量积小波紧框架,提出了基于香农熵自适应确定最优小波紧框架分解层数以及改进的Normal Shrink自适应阈值算法,并给出了图像去噪实例和结果分析,获得了理想的数值结果,显示了本文方法的有效性.In this paper, we research the problem of image denoising. Via the use of the smoothing cofactor-conformality method, it constructs the bivariate and sextic spline function in spline space S64（△（mn）（2））, and while do it as scaling function, the non-tensor product tight wavelet frame is constructed based on the unitary extension principe. Then we propose the algorithm of the optimal decomposition levels of tight wavelet frame is self-adaptive determined based on the shannon entropy and the modified Normal Shrink self-adaptive threshold algo-rithm by using the non-tensor product tight wavelet frame above, and offer the cases of image denoising and result analysis. The ideal numerical results are obtained, which verify the validity of this algorithm.

关 键 词：非张量积小波紧框架 最优分解层数 自适应阈值 图像去噪 

分 类 号：O29[理学—应用数学]