低秩恢复模型与快速算法及其在遥感图像特征提取中应用的研究

Image feature analysis and extraction is a very important and difficult research topic in the field of image processing. Due to the diversity and complexity of the image feature, the traditional method of image feature extraction is unable to satisfy the real application with respect to the effect and efficiency. The low-rank models and algorithms, which utilize a specially mathematical property of the sparsity of the image data- - low-rank, have developed as a novel methodology in this field. However, the proposed low-rank models are almost based on the assumption of square error, and unable to deal with the general case. Based on the .theory of statistics learning, regularization and Bayesian methods, and combining the problem of the feature extraction of the remote-sensing image, this project research new low-rank models with lower complexity, better recovered effect and more extensive application; meanwhile, the Nesterov convex optimization method is further developed and fast and robust algorithms with globally geometry-convergence property are designed based on the strong convexity of the augumented model, the restricted strong-convexity of the dual models and Nesterov accelerating technology based on the strongly convex property. The proposed methods are verified through large amount of imitation tests. The results of the project can be used widely in national defense and civil producing industries such as satellite observations, earth observation and monitoring.

图像特征分析与提取是图像处理领域中重要的经典研究问题和难题。由于图像特征的多样性和复杂特性，传统的特征提取方法其效果和效率很难满足实际需求。低秩模型与算法是利用图像数据稀疏性的一个重要数学性质－数据的低秩性建立起来的图像特征提取新方法。但现有低秩模型大都基于均方差假设，不能处理一般的特征提取问题。本项目基于统计学习理论、正则化理论、贝叶斯分析等方法，并结合遥感图像特征提取的实际，研究低复杂度，恢复效果好，具有广泛应用的低秩恢复模型；通过深入研究Nesterov凸优化方法，结合增广模型的强凸性、其对偶模型的限制强凸性、以及基于强凸性的Nesterov加速技术设计具有最优收敛系数的全局几何收敛率快速稳健算法。通过大量仿真实验验证方法的有效性。本项目成果可以广泛应用于卫星遥感观测、对地侦查以及监控等等国防和民用领域。

按照项目申请书中所列的研究内容和研究计划，本项目研究了遥感图像的低秩稀疏模型和低复杂度算法及其收敛性。过去四年，围绕上述紧密相关的研究内容，项目组成员通力合作、协同攻关，共发表高水平SCI论文20篇，完成了项目中的预期计划。具体而言，取得了如下成果：.（1）模型方面的成果：设计了适用于遥感图像特征提取的低秩恢复模型以及相应的图像去噪和分割的快速算法；.（2）理论与算法成果：建立了增广的低秩恢复模型的正则化理论，推导了增广模型中的增广参数的计算公式，设计了具有全局几何收敛率的奇异值阈值算法及算法软件，及相应的加速算法，设计了全局几何收敛率算法及其相应的算法软件；.（3）制作了基于低秩模型与快速稳健算法的遥感图像特征提取演示验证系统。