Hyperspectral Image Unmixing Algorithms Based On Distribution Distance And Rate Distortion Theory

The characteristics of hyperspectral image data,such as low spatial resolution and spectral variability,cause the mixed pixel problem that seriously limits the accurate applications of hyperspectral images(HSIs).Although the deep learning algorithms show notable strength in solving the mixed pixel problem,there are still challenges such as difficulty in fully fusing prior information and missing important endmember information,resulting in poor unmixing performance.To address the above problems,this dissertation designs a series of effective HSI unmixing algorithms based on the autoencoder framework by combining the integral probability metric with rate-distortion theory.The specific research work is summarized as follows:(1)To address the problem that current unmixing algorithms are difficult to fully fuse prior information leading to low unmixing performance,based on integral probability metric,a joint metric neural network framework for HSI unmixing is constructed by introducing Wasserstein distance and deep metric learning and combining with spectral angle distance(SAD).The proposed framework consists of two parts: a three-layer fully-connected autoencoder is used for endmember extraction and abundance estimation? a three-layer fullyconnected neural network called discriminator is adopted to implicitly compute the Wasserstein distance between input spectrum and reconstructed spectrum.Simultaneously,in the discriminator,the deep metric learning is adopted to match the intermediate-layer features of input spectra with that of reconstructed one.The Wasserstein distance and feature matching are regarded as regularization terms added to the underlying SAD loss so as to be a new loss function.Model analysis demonstrates that these two regularization terms can additionally provide useful gradient information that promotes the autoencoder to reach a solution with better unmixing performance.Experimental results show that the proposed algorithm can achieve excellent performance on HSI unmixing.(2)To address the problem of high computational cost of Wasserstein distance,we adopt the Maximum Mean Discrepancy(MMD)instead of Wasserstein distance to train the unmixing autoencoder,and propose an HSI unmixing algorithm based on a probability-metric autoencoder.We first make a theoretical analysis of sample complexity about both Wasserstein distance and MMD,and show that adopting the MMD to train the unmixing autoencoder is a more effective way when the data dimensionality is high.This is made possible by the fact that MMD can be computed explicitly and its sample complexity is not affected by the data dimensionality.Then,the proposed SAD-MMD loss is applied to three types of autoencoder framework,the ablation experimental results show that combining SAD and MMD as the final loss function can boost the unmixing performance a lot compared with the single SAD loss.Finally,we investigate the impacts of batch size and sum-to-one constraint on unmixing performance and guidelines for setting these two parameters in practical application scenarios are given.(3)Aim at the problem that spectral variability leads to a single abundance map obtained by a general unmixing algorithm,based on rate distortion theory,an unmixing algorithm is developed for large-scale HSI data by introducing lossy coding rate(LCR)to measure the diversity of the abundance map.We first conduct lossy coding of the abundance vectors,then combine SAD loss with Mean Square Error(MSE)as a new loss function,and maximize the lossy coding rate to train the unmixing autoencoder,which drives the learned abundance maps own diversity and thus boosts the unmixing performance.In addition,the proposed SAD-MSE-LCR loss is applied to the shallow fully-connected and deep fully-connected autoencoders,experimental results show that this loss function is not only robust to the batch size of the training data,but also maintains excellent unmixing performance.