结构保持的图像非局部分数阶数值模型与算法研究

项目名称： 结构保持的图像非局部分数阶数值模型与算法研究

项目编号： No.61301243

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 无线电电子学、电信技术

项目作者： 江玲玲

作者单位： 中国石油大学（华东）

项目金额： 24万元

中文摘要： 分数阶变分模型能很好地保持图像的边缘、纹理等重要结构特征，较整数阶变分模型在图像恢复时优越，逐渐成为信号和图像处理领域中崭新的研究方法。但分数阶的理论分析和算法设计较困难，如何构建好的优化模型和高效的数值算法是一个非常有意义的研究课题。本项目在前期整数阶变分PDE和分数阶稳定性分析的基础上拟对如下问题展开研究：(1)在Meyer的振荡分量建模的理论框架下，结合有界变差空间(BV)和分数阶导数，构建分数阶有界变差空间，设计各种分数阶正则的图像恢复模型；(2) 利用图像非局部不连续性测度的概念及分数阶微分理论，通过选择不同势函数的非局部正则化泛函，建立非局部的分数阶变分模型；(3) 研究小波、曲线波等稀疏表示工具和分数阶多尺度空间的内在联系，发挥变换域上分数阶变分问题的优势。本项目立足模型选择和设计高效的数值算法，具有一定的开创性和前沿性，相信会推动其在信息科学领域的应用与发展。

中文关键词： 图像恢复；分数阶全变分；小波；非凸非光滑正则化；

英文摘要： Fractional-order variational models can preserve useful structures such as edges and textures well than integer-order variational models in image restoration. So this method becomes one of the popular techniques. However, fractional derivative has high computational complexity. How to build good models and design efficient algorithms is a significant research subject. In this project, based on integer-order variational PDE and fractional stability analysis,it mainly makes researches on the following issue:(1) Based on the theory of Meyer's oscillatory component modeling and combined with fractional-order derivative and function space of bounded variation，the fractional-order function space of bounded variation is proposed. Some fractional-order regularization models for image restoration are proposed;(2)Using the conceptions of non-local discontinuity of image and fractional differential,and by different examples of non-local regularization energy functional,non-local fractional variational models are proposed; (3) Internal relations among wavelet, curvelet and fractional-order scale space are studied and the advantages of fractional-order variational in transform domain are developed. The subject mainly proposes the fractional-order regularization model and gives some fast algorithms.In information science, ou

英文关键词： Image restoration；fractional-order total variation；wavelet；nonconvex and nonsmooth regularization；