MultiHU-TD: Multifeature Hyperspectral Unmixing Based on Tensor Decomposition

• Published in: IEEE transactions on geoscience and remote sensing Vol. 61; pp. 1 - 21
• Main Authors: Jouni, Mohamad, Mura, Mauro Dalla, Drumetz, Lucas, Comon, Pierre
• Format: Journal Article
• Language: English
• Published: New York IEEE 2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Blind source separation (BSS); Cost function; Decomposition; extended linear mixing model (ELMM); Feature extraction; Frameworks; Hyperspectral imaging; hyperspectral unmixing (HU); interpretability; Mathematical analysis; Mathematical models; Mathematical morphology; Matrix decomposition; Medical services; Morphology; Optimization; tensor decomposition; Tensors
• ISSN: 0196-2892; 1558-0644
• DOI: 10.1109/TGRS.2023.3314218

Hyperspectral unmixing allows representing mixed pixels as a set of pure materials weighted by their abundances. Spectral features alone are often insufficient, so it is common to rely on other features of the scene. Matrix models become insufficient when the hyperspectral image (HSI) is represented as a high-order tensor with additional features in a multimodal, multifeature framework. Tensor models such as canonical polyadic decomposition allow for this kind of unmixing but lack a general framework and interpretability of the results. In this article, we propose an interpretable methodological framework for low-rank multifeature hyperspectral unmixing based on tensor decomposition (MultiHU-TD) that incorporates the abundance sum-to-one constraint in the alternating optimization alternating direction method of multipliers (ADMM) algorithm and provide in-depth mathematical, physical, and graphical interpretation and connections with the extended linear mixing model. As additional features, we propose to incorporate mathematical morphology and reframe a previous work on neighborhood patches within MultiHU-TD. Experiments on real HSIs showcase the interpretability of the model and the analysis of the results. Python and MATLAB implementations are made available on GitHub.