Solving Spectrum Unmixing as a Multi-Task Bayesian Inverse Problem with Latent Factors for Endmember Variability

With the increasing customization of spectrometers, spectral unmixing has become a widely used technique in fields such as remote sensing, textiles, and environmental protection. However, endmember variability is a common issue for unmixing, where changes in lighting, atmospheric, temporal conditions, or the intrinsic spectral characteristics of materials, can all result in variations in the measured spectrum. Recent studies have employed deep neural networks to tackle endmember variability. However, these approaches rely on generic networks to implicitly resolve the issue, which struggles with the ill-posed nature and lack of effective convergence constraints for endmember variability. This paper proposes a streamlined multi-task learning model to rectify this problem, incorporating abundance regression and multi-label classification with Unmixing as a Bayesian Inverse Problem, denoted as BIPU. To address the issue of the ill-posed nature, the uncertainty of unmixing is quantified and minimized through the Laplace approximation in a Bayesian inverse solver. In addition, to improve convergence under the influence of endmember variability, the paper introduces two types of constraints. The first separates background factors of variants from the initial factors for each endmember, while the second identifies and eliminates the influence of non-existent endmembers via multi-label classification during convergence. The effectiveness of this model is demonstrated not only on a self-collected near-infrared spectral textile dataset (FENIR), but also on three commonly used remote sensing hyperspectral image datasets, where it achieves state-of-the-art unmixing performance and exhibits strong generalization capabilities.