二维四向小波变分泛函及模糊图像恢复理论研究  

Study on the Theory of Two-dimensional Four-way Wavelet Variational Function and Fuzzy Image Restoration

作　　者：马瑞瑞 王刚[1] 张静[1] Ma Ruirui;Wang Gang;Zhang Jing(School of Mathematical Sciences,Xinjiang Normal University,Urumqi 830054,China)

机构地区：[1]新疆师范大学数学科学学院,新疆乌鲁木齐830054

出　　处：《甘肃科学学报》2021年第6期10-15,共6页Journal of Gansu Sciences

基　　金：新疆师范大学优秀青年教师科研启动基金资助项目(XJNU202014)。

摘　　要：在双向小波构造理论、二维四向小波理论及图像处理基础上,研究了二维四向小波基的稳定性与光滑性、二维四向小波基的变分问题与最小化、二维四向小波变分泛函冗余度及模糊图像恢复理论问题。采用有关二维四向小波的分解算法,从理论上对二维四向加细函数的图像进行分解,得到了二维四向小波基的变分问题产生的一种参数化的解,以及二维四向小波基下模糊的图像恢复的理论研究结果。Based on bidirectional wavelet construction theory,two-dimensional four-way wavelet theory and image processing,the stability and smoothness of two-dimensional four-way wavelet basis,the variational problems and minimization of two-dimensional four-way wavelet basis,the redundancy of two-dimensional four-way wavelet variational functional and fuzzy image restoration theory are studied.In the process of the research,the image decomposition of the two-dimensional four-way additive function is studied theoretically by using the decomposition algorithm of the two-dimensional four-way wavelet,and a parameterized solution of the variational problem of the two-dimensional four-way wavelet basis and the theoretical research result of the fuzzy image restoration under the two-dimensional four-way wavelet basis are obtained.

关 键 词：二维四向小波基 稳定性与光滑性 变分泛函 模糊图像恢复 

分 类 号：O174.2[理学—数学]