数据驱动的混合逆问题cGANs回归及其在高光谱数据解混中的应用

Due to the rough spatial resolution, most of the pixels acquired by hyperspectral remote sensors are composed of several ground materials, which are well known as mixed pixels or mixtures. The widely presence of mixtures influences the performance of hyperspectral data classification and target recognition. Therefore, spectral unmixing, which extracts fractional abundance of pure materials (known as endmember) within a pixel, has been developed to solve such mixed-pixel problems. Regularization is a widely used technique throughout unmixing of hyperspectral data. From a computational perspective, regularization can lend stability to the optimization problem and can lead to algorithmic speed-ups. For decades, con¬structing regularization required careful engineering and considerable domain expertise to design a proper regularization term. In this project, the restricted isometry property (RIP) of the endmember matrix is studied in detail. The abundance vector reconstruction is treated as a regression problem mapping from spectral vector to abundance vector. The regression network is constructed via cGANs. Some abundance vectors and training samples can be obtained by a pre-unmixing. The basic requirement of the training samples is that the constructed mixed hyperspectral data should follow the same distribution with the real hyperspectral data. In addition, spatial correlation among pixels is considered in this project. It is assumed that spatial neighbors most likely possess a similar abundance vector as the testing pixel in the center of the neighborhood. However how to choose a proper size of the neighborhood is a key issue of the deep learning unmixing. Ensemble methods can thus reduce the risk of selecting the wrong model by aggregating all these candidate models. All the outputs of the deep learning unmixing network are put into a vector, and an ELM is trained to find a better result. Extensive experiment results, with both synthetic and real images, illustrate the generality and effectiveness of theses schemes.The research of this project will solve the nonlinear unmixing of hyperspectral data and promote the cross-integration between mathematics，machine learning and remote sensing data processing.

从空间分辨率低、地物谱信息动态变化的复杂高光谱数据中准确快速地提取地物目标的亚像元信息，是当前遥感领域的难题之一。本课题针对正则混合逆问题求解中的正则项构造难和正则优化问题求解速度慢等瓶颈问题，将混合逆问题转化为数据驱动的函数逼近问题。利用生成网络和判别网络的博弈对抗机制，建立高阶混合模型的cGANs回归架构，实现混合像元的模拟和隐函数逼近。面向高光谱数据解混，提出cGANs高光谱回归解混，突破端元提取、混合模式提取和表示、混合像元的生成、混合逆问题的网络回归等关键技术，最后通过合成数据、AVIRIS实测数据以及我国高分系列卫星的获取高光谱数据验证模型和方法有效性，打破了空间分辨率对高光谱数据解译的限制，推动数学、机器学习与遥感数据处理的交叉融合。

本课题针对正则逆问题求解中正则项构造难、混合优化问题求解速度慢以及样本手工标注费时费力等瓶颈问题，将解混转化为数据驱动的函数逼近问题，建立深度网络（AE，CNN、GAN和Transformer）逆问题回归模型，混合模式表示、混合像元的生成、混合逆问题的网络回归和小样本高光谱分类等关键技术方面取得突破性进展。.在高光谱图像解混方面，提出基于空间和光谱相似性的卷积神经网络(CNN)的高光谱解混、基于生成对抗网络（GAN）的高光谱解混、基于自编码网络的广义双线性模型解混、基于卷积神经网络的条件生成对抗网络空谱联合解混和基于Patch Transformer 的条件生成对抗网络空谱联合解混，利用生成网络和判别网络的博弈对抗机制以及先验知识，生成和实际高光谱数据同分布的训练样本，掘邻近高光谱混合像元丰度向量之间的相关性，最后借助深度网络强大的函数逼近能力逼近特征向量或谱向量与丰度向量之间的隐函数关系。在高光谱图像分类方面，提出基于生成对抗网络数据增强的高光谱图像分类算法和基于对抗表示学习的高光谱图像分类算法等方法，改进生成对抗网络进行，设计了基于辅助分类器的带梯度惩罚的生成对抗网络模型，通过条件熵引入无标签样本对模型进行半监督对抗训练，使编码器提取的特征更适合于分类任务。最后通过人工合成的高光谱数据和网上公开的AVIRIS 高光谱数据验证新模型和新方法的可行性和有效性。实验结果证明了所提算法相比于其他先进算法更有优势，尤其是在样本数目较少的情况下，这种优势更为明显。

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