图像恢复的非局部稀疏建模理论及算法研究

项目名称： 图像恢复的非局部稀疏建模理论及算法研究

项目编号： No.61201431

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 电子学与信息系统

项目作者： 姜东焕

作者单位： 山东科技大学

项目金额： 24万元

中文摘要： 本项目拟以变分正则化方法为工具将非局部滤波和图像的小波稀疏表示有机结合，构造非局部的稀疏正则项对图像建模,研究探讨新的图像恢复模型及其快速算法。该课题主要研究以下几个问题：一是根据Besov空间的理论创建非局部Besov空间的相关理论，定义该空间的范数，用它作为图像的光滑性约束进行建模，建立非局部的变分泛函及研究图像的非局部Besov范数在小波域的等价形式，然后利用等价形式在小波变换域中对该泛函进行求解，建立非局部的稀疏图像恢复模型。二是把图像分解成卡通和纹理部分，对每一部分分别根据它们的特征选择合适的非局部稀疏正则项建立变分泛函进行恢复，然后将两恢复结果结合起来即为恢复后的图像。三是为以上所建两类图像恢复模型寻求稳健和收敛的快速算法。课题的研究将非局部滤波和小波稀疏表示有机地联系起来，拓宽非局部滤波算法的应用范围，丰富非局部图像处理理论，为图像反问题的研究提供新的理论基础和方法借鉴。

中文关键词： 图像恢复；非局部滤波；变分正则化；分裂Bregman；图像分割

英文摘要： This project intends to combine nonlocal filtering with sparse wavelet representation using regularization method and construct nonlocal sparse regularization term for image modeling, then study new models for image restoration and their fast algorithms. The research contents include: First, the theory of Besov space is extended to create nonlocal Besov space. The norm of nonlocal Besov space is defined and is used to model image as smoothness constraints. The nonlocal variational functional and the equivalent form of nonlocal Besov norm in the wavelet domain are established. Then the research on the variational functional is converted to the wavelet domain, thus the nonlocal sparse image restoration model is constructed. Second, the image is decomposed into cartoon and texture. Nonlocal sparse regularization terms are selected respectively for each part to construct the variational functional, and then the image restored is obtained by combining the results of two recovery. Third, we seek a fast and stable algorithm with convergence for the above two types of image restoration model. Study of nonlocal filtering and wavelet sparse representation has broaden the scope of application of nonlocal filtering algorithm, enriched the nonlocal theory for image processing and provided new theoretical basis and method for

英文关键词： image restoration；nonlocal filter；variational regularization；split- Bregman；image segmentation