过完备稀疏表示及其在图像超分辨率恢复中的应用研究

The restoration of Low resolution images has been a challenging issue to this day.And in recent years, the image super-resolution restoration via sparse representation has been of a new trend of research and a hot toppic. On the basis of the research on over-complete sparse coding of the receptive fields of simple cells in the mammalian primary visual cortex in brain, also known as V1, and the mechine learning algorihtms, this project will model a new sparse dictionary and explore efficient sparse optimized factorization algorithm, further, the image restoration problems of two class of low-resolution images, namely millimeter wave images and medical images by using the researh results above-mentioned are discussed. Firstly, according to the theory of image sparse representation,combined mature reduncdant dictionary design methods,and considered the sparse priori constraint of images, new computational models of sparse dictionary or multiple sparse dictionary are designed. And then, considered the classicial dictionary learning algorithms, such as the regularization orthotropic matching pursuit (ROMP), generalized principal component analysis (PCA), K-mean based singular value decomposition (K-SVD) and so on, the fast sparse optimized factorization algorithms are discussed. Further,on the basis of the proprocessing research of low-resolution images, combined the transform of contourlet and doule-tree complex wavelet, projection onto convex sets (POCS), partial differential equations (PDEs) and other image restoration methods, and utilized the information fusion technique between features of images, a class of novel image super-resolution restoration methods based on spare dictionary with visual property are explored. The reseach results of this project not only provide a new path for low-resolution images' processing, but also promote the develop of intelligent information technology.

低分辨率图像的恢复一直是个挑战性的课题，而基于稀疏表示的图像超分辨率恢复近年来成为一个新的研究方向和研究热点。本项目将在研究人眼初级视觉系统主视皮层V1区神经细胞感受野的过完备稀疏编码和机器学习算法的基础上，构造过完备的稀疏字典并探索其有效的稀疏优化分解算法，进一步应用于毫米波和医学两类低分辨率图像的恢复。首先，根据图像稀疏表示理论，结合成熟的冗余字典设计方法，考虑图像的稀疏先验约束，构造新颖的稀疏及多重稀疏字典计算模型；然后结合正则化正交匹配追踪（ROMP）、广义PCA、K-SVD等经典字典训练算法，研究快速的稀疏优化算法；进一步在低分辨率图像预处理基础上，结合轮廓波、双数复小波变换、凸集投影、偏微分方程等算法，利用特征级信息融合手段，探索新的基于视觉特性的稀疏字典的超分辨率恢复方法。本项目的开展为低分辨率图像的处理提供了新的途径，同时也促了智能信息技术的发展。

本项目按照既定的研究计划进行，较好地完成了预定的研究内容并有所拓展。该项目针对基于稀疏表示的图像超分辨率恢复问题，围绕过完备稀疏字典模型的构建、低分辨率图像预处理、稀疏优化分解方法、超分辨率图像恢复方法等方面展开研究，取得了一定的重要研究成果。研究工作主要包括以下几个方面：.（1）建模并优化学习了一类考虑图像特征约束的非负稀疏表示模型。考虑特征线性可分性，提出了一种基于离散度约束的非负稀疏编码模型，该模型有效提高了特征识别精度；基于非负矩阵分解，考虑图像局部特征，提出了一种局部非负稀疏表示模型；考虑残差图像细节信息，提出了一种基于二阶段分段学习稀疏表示字典模型的方法，可以有效表示图像的稀疏结构。.（2）针对低分辨率图像的特点，考虑未知噪声和非线性特征的影响，结合模糊神经网络、核函数学习、多任务支持向量机、稀疏表示及偏微分方程的自适应消噪特性等算法的优势，提出多种图像预处理方法，这些方法可以有效消除噪声影响、提高低分辨率图像的轮廓特征和目视效果；.（3）为了提高低分辨率图像的恢复质量，本项目在图像超分辨率算法中引入基于图像特征的稀疏字典学习，考虑高分辨率和低分辨率图像特征的稀疏字典对、结构特征聚类字典、图像特征的多重稀疏字典学习、快速稀疏优化分解算法等，提出了多种基于稀疏表示的图像超分辨率恢复方法。.本项目的研究成果为毫米波图像和医学图像等这类低分辨率图像提供了一种有效的手段，所提出的研究方法可以拓展应用于红外图像、雷达图像、遥感图像的处理，有非常实用的研究意义。