A Probability Metric-Based Autoencoder for Hyperspectral Unmixing

In recent years, hyperspectral unmixing (HU) has been a crucial preprocess in hyperspectral imagery analysis. Current learning-based methods of HU are built on the autoencoder framework. Most of them hold a pointwise loss function only comparing the individual difference without the overall difference. As a remedy, we propose a probability metric-based autoencoder (PMAE) for HU. Specifically, we combine a distribution distance called maximum mean discrepancy (MMD) with underlying loss spectral angle distance (SAD) as the final loss function for training the unmixing autoencoder. The MMD can be seen as a regularization that is designed to match all orders of statistics between the input spectrums and the reconstructed spectrums. The SAD is to compare the individual difference, while the MMD compares the overall difference. Combing these two points, we can obtain more prior information to guide the autoencoder training toward boosting the unmixing performance. In order to validate this viewpoint, we conduct model analysis and a series of ablation studies, showing that adding the MMD into the autoencoder unmixing model, indeed, boosts the unmixing performance a lot compared to the single SAD objective. Experimental results on five real hyperspectral scenes demonstrate the effectiveness and competitiveness of the proposed PMAE compared with several classical and learning-based approaches.