空间约束下多字典学习的形态学成分分析

项目名称： 空间约束下多字典学习的形态学成分分析

项目编号： No.61271294

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 无线电电子学、电信技术

项目作者： 冯象初

作者单位： 西安电子科技大学

项目金额： 65万元

中文摘要： 数字图像处理中的形态学成分分析方法（MCA）利用解析构造的基函数为字典，如小波、DCT等，实现图像的结构和纹理成分的分解。本项目针对MCA的两个基本问题展开研究。（1）MCA中基函数的选择是先验的。本项目计划通过空间引导方法，利用计算调和分析中的分解空间作为约束，通过自适应学习方法，建立基于字典学习和数据驱动的新的更有效分解模型和算法。（2）MCA中的字典是单一的。针对图像不同区域的特征，本项目计划建立相应约束下的多字典学习方法。本项目将要研究的主要问题包括：模型的建立和理论分析、合适的引导空间的选择、字典约束的优化形式和相应快速算法的设计等。在发展MCA理论的基础上，我们将给出新方法在图像恢复（去噪、插值、修补）、边缘检测、盲源分离等问题上的应用。本课题预期在理论上有突破，方法和技术上有创新，为该方法的实际应用奠定理论和技术基础。

中文关键词： 图像去噪；图像增强；图像融合；字典学习；稀疏表示

英文摘要： Usually a complex system is consisted of many simple systems. It will be helpful if we can decompose a complex system into its components. For example, in the image processing fields, a digital image is constructed by cantoon part and texture part.It will be more efficient to deal with these two parts separetily than to deal with the image as a whole. Morphological component analysis(MCA) is the frontier in the image processing field. It is a very important and useful method both in the theory and in the engineering aspects. In fact, MCA decompose a given image into different morphological parts based on the basis constructed before, such as wavelet and DCT. On the other hand, in the field of numerical harmonic analysis, the image decomposition is made by the use of different spaces. Based on the dictionary learning, in this project, we plan to combine the two methods above together and construct a novel model. Dictionary learning is more adaptive than the dictionary analitically constructed. To the decomposition problem, the dictionary learning should be guided by the proper spaces which were studied in the harmonic analysis field. Furthor more, in order to learn multiple dictionaries, the constraints are needed to ensure the existence of the non-trivial solutions, which makes the law-rank constraint dictionar

英文关键词： Image denoising；Image enhancement；Image fusion；Dictionary learning；Sparse representation