高光谱图像稀疏解混模型及其快速算法研究

Unmixing is a process of detecting the containing materials and their corresponding fractions (abundances) from a given hyperspectral image. Generally, there are three disadvantages in existing unmixing methods: firstly, rather than the true sparse solution, the common solution towards the sparsity of abundances is to solve its equivalent solution or approximate solution under certain conditions; secondly, the spatial and spectral information of the hyperspectral image are not received enough attention in unmixing; finally, there are rare methods that can unmix with both high precision and efficiency. In this proposal, to avoid above drawbacks, we will use sparse representation and optimization techniques to develop some novel methods as well as the corresponding algorithms for semi-supervised unmixing. Our novelties lie in that 1) the minimization problem with L0 norm is converted into an equivalent matrix rank minimization problem or a truncated L1 norm minimization problem; 2) some unmixing methods will be developed based on some properties of the abundances and the spatial and spectral information of the hyperspectral image; 3) the unmixing optimization problem will be divided into several parts based on the variable substitution and operator splitting, and will be addressed efficiently by using an alternative minimization algorithm. We will conduct extensive numerical experiments to demonstrate the stability and efficiency of the proposed approaches, using both practical measurement and remotely sensed data. Preliminary results show that our ideas are feasible. It can be expected that our unmixing methods will outperform most of the state-of-the-art methods. The ultimate results of this project will provide some new ideas for hyperspectral unmixing.

混合像元分解（亦称“解混”）是求解高光谱遥感图像中每个像元所含物质及其成分比例（丰度）的过程。现有解混方法总体而言有如下缺陷：多是在一定条件下求丰度稀疏性的等价或近似表示，而不涉及真正稀疏解；对高光谱图像结构信息挖掘不够；高精度和高效率解混难以兼得。为避免以上问题，本项目将运用稀疏表示和优化等手段，发展出一套新的半监督高光谱解混模型及算法。其创新在于：将0范数极值问题转换成等价的矩阵秩或截断1范数的极值问题；结合高光谱图像空间、光谱信息和丰度特性提出一系列新解混模型；采用交替迭代法，结合变量替换和算子分裂方式将问题分解，实现快速解混。为验证模型和算法的稳定与精确性，本项目将采用野外实测、卫星遥感等多源数据对该套方法进行全面验证和比较。初步试验表明，本项目研究思路可行。预期结果总体而言将优于当前各主要解混算法。本项目的最终成果将为混合像元分解提供新的思路和途径。

高光谱遥感图像解混技术对于大量科学研究和实际应用均具有重要价值，也一直是遥感应用研究的难点和热点问题。本项目针对高光谱遥感图像混合像元分解问题，在考虑高光谱图像空间与光谱结构信息、丰度物理特性的基础上，探索了新的高光谱解混方法，建立起了一系列包括结构相似性、稀疏性等约束的优化模型，探讨了模型在理论上的正确性，研究了模型的具体快速算法，并运用大量数据对该模型进行了验证，在解混模型与算法研发、精确度与鲁棒性提高等方面均取得了进展。.项目研究进展顺利，在理论研究方面，围绕1)高光谱图像像元丰度的稀疏表示，2) 混合像元分解的优化新模型，3）基于算子分裂法的快速解混算法，4）解混模型及其算法验证等4个方向展开了重点研究。在理论方法上取得了多项突破，圆满完成了各项研究任务，实现了预期研究目标。在研究成果方面，课题组成员已出版学术论文5篇（SCI论文4篇，ECCV会议论文1篇），已接收即将发表SCI论文1篇，包含2篇CCFA类论文。在学术合作与交流方面，分别到香港浸会大学、香港中文大学进行短期访问6人次，邀请国内外学者交流访问2人次。在人才培养方面，联合培养博士研究生1人、硕士研究生2人。