SWAN: Self-supervised Wavelet Neural Network for Hyperspectral Image Unmixing

TL;DR

The paper tackles blind hyperspectral unmixing under limited ground-truth data by introducing SWAN, a three-stage self-supervised framework that operates in a Biorthogonal wavelet domain to learn endmembers $ extbf{M}$ and abundances $ extbf{A}$. It learns a mapping in the wavelet space via SWANencoder, reconstructs coefficients through SWANdecoder, and imposes a physics-inspired SWANforward to capture data acquisition effects, with a three-part acquisition-domain loss and regularizers. The approach leverages sparse, multi-scale wavelet representations to reveal latent symmetries, enabling a compact model (~50k parameters) and robust learning without ground-truth unmixed components. Experiments on two synthetic datasets and three real hyperspectral datasets show SWAN achieving superior or competitive quantitative metrics (RMSE, SAD, SID) while maintaining resilience to noise, highlighting its potential for resource-constrained, real-world unmixing tasks.

Abstract

In this article, we present SWAN: a three-stage, self-supervised wavelet neural network for joint estimation of endmembers and abundances from hyperspectral imagery. The contiguous and overlapping hyperspectral band images are first expanded to Biorthogonal wavelet basis space that provides sparse, distributed, and multi-scale representations. The idea is to exploit latent symmetries from thus obtained invariant and covariant features using a self-supervised learning paradigm. The first stage, SWANencoder maps the input wavelet coefficients to a compact lower-dimensional latent space. The second stage, SWANdecoder uses the derived latent representation to reconstruct the input wavelet coefficients. Interestingly, the third stage SWANforward learns the underlying physics of the hyperspectral image. A three-stage combined loss function is formulated in the image acquisition domain that eliminates the need for ground truth and enables self-supervised training. Adam is employed for optimizing the proposed loss function, while Sigmoid with a dropout of 0.3 is incorporated to avoid possible overfitting. Kernel regularizers bound the magnitudes and preserve spatial variations in the estimated endmember coefficients. The output of SWANencoder represents estimated abundance maps during inference, while weights of SWANdecoder are retrieved to extract endmembers. Experiments are conducted on two benchmark synthetic data sets with different signal-to-noise ratios as well as on three real benchmark hyperspectral data sets while comparing the results with several state-of-the-art neural network-based unmixing methods. The qualitative, quantitative, and ablation results show performance enhancement by learning a resilient unmixing function as well as promoting self-supervision and compact network parameters for practical applications.

Figures (15)

• Figure 1: Function map of problem set-up
• Figure 2: Schematic diagram of the proposed SWAN for hyperspectral image unmixing.
• Figure 3: Detailed neural architecture design of the proposed SWAN in Fig. \ref{['proposed_network_architecture']}.
• Figure 4: Compressibility of hyperspectral imagery AVIRIS Cuprite datasets, HYDICE Urban datasets, Samson datasets, and AVIRIS Jasper Ridge datasets: The images are represented using bior 3.3 wavelet at optimum nodes of decomposition. It can be observed that bior 3.3 coefficients optimally decay as per the power law candes2005signal. This helps represent hyperspectral images in a compact form.
• Figure 5: Endmembers and their respective locations are marked on the mean image: (a) Synthetic HSI data 1: Am-Ammonioalunite, An-Andradite, Br-Brucite, and (b) Synthetic HSI data 2: A-Asphalt, B-Brick, F-Fiberglass, S-Sheetmetal, V-Vinylplastic.