Diffusion Posterior Sampler for Hyperspectral Unmixing with Spectral Variability Modeling

Abstract: Linear spectral mixture models (LMM) provide a concise form to disentangle the constituent materials (endmembers) and their corresponding proportions (abundance) in a single pixel. The critical challenges are how to model the spectral prior distribution and spectral variability. Prior knowledge and spectral variability can be rigorously modeled under the Bayesian framework, where posterior estimation of Abundance is derived by combining observed data with endmember prior distribution. Considering the key challenges and the advantages of the Bayesian framework, a novel method using a diffusion posterior sampler for semiblind unmixing, denoted as DPS4Un, is proposed to deal with these challenges with the following features: (1) we view the pretrained conditional spectrum diffusion model as a posterior sampler, which can combine the learned endmember prior with observation to get the refined abundance distribution. (2) Instead of using the existing spectral library as prior, which may raise bias, we establish the image-based endmember bundles within superpixels, which are used to train the endmember prior learner with diffusion model. Superpixels make sure the sub-scene is more homogeneous. (3) Instead of using the image-level data consistency constraint, the superpixel-based data fidelity term is proposed. (4) The endmember is initialized as Gaussian noise for each superpixel region, DPS4Un iteratively updates the abundance and endmember, contributing to spectral variability modeling. The experimental results on three real-world benchmark datasets demonstrate that DPS4Un outperforms the state-of-the-art hyperspectral unmixing methods.