An Augmented Linear Mixing Model to Address Spectral Variability for Hyperspectral Unmixing (1810.12000v1)

Abstract: Hyperspectral imagery collected from airborne or satellite sources inevitably suffers from spectral variability, making it difficult for spectral unmixing to accurately estimate abundance maps. The classical unmixing model, the linear mixing model (LMM), generally fails to handle this sticky issue effectively. To this end, we propose a novel spectral mixture model, called the augmented linear mixing model (ALMM), to address spectral variability by applying a data-driven learning strategy in inverse problems of hyperspectral unmixing. The proposed approach models the main spectral variability (i.e., scaling factors) generated by variations in illumination or typography separately by means of the endmember dictionary. It then models other spectral variabilities caused by environmental conditions (e.g., local temperature and humidity, atmospheric effects) and instrumental configurations (e.g., sensor noise), as well as material nonlinear mixing effects, by introducing a spectral variability dictionary. To effectively run the data-driven learning strategy, we also propose a reasonable prior knowledge for the spectral variability dictionary, whose atoms are assumed to be low-coherent with spectral signatures of endmembers, which leads to a well-known low coherence dictionary learning problem. Thus, a dictionary learning technique is embedded in the framework of spectral unmixing so that the algorithm can learn the spectral variability dictionary and estimate the abundance maps simultaneously. Extensive experiments on synthetic and real datasets are performed to demonstrate the superiority and effectiveness of the proposed method in comparison with previous state-of-the-art methods.

• The paper proposes a novel ALMM that integrates scaling factors and a spectral variability dictionary to better model environmental effects.
• It employs a data-driven dictionary learning strategy with ADMM optimization to jointly estimate abundance maps and spectral variability.
• Numerical experiments show significant improvements in abundance estimation accuracy over traditional methods on both synthetic and real datasets.

An Augmented Linear Mixing Model for Hyperspectral Unmixing

The paper presents a novel approach for hyperspectral unmixing by introducing an Augmented Linear Mixing Model (ALMM) to tackle spectral variability issues inherent in hyperspectral imagery. The classical Linear Mixing Model (LMM) often falls short in effectively estimating abundance maps due to spectral variability arising from factors like illumination changes, topography, and atmospheric conditions. The proposed ALMM aims to address these limitations through a data-driven learning strategy integrated within hyperspectral unmixing.

Key Contributions

1. Modeling Spectral Variability: The ALMM incorporates scaling factors modeled by an endmember dictionary alongside a spectral variability dictionary to address changes due to environmental conditions, sensor noise, and nonlinear mixing effects. This dual approach enables a more comprehensive handling of spectral variabilities.
2. Data-Driven Learning: By embedding a dictionary learning technique within the framework, the algorithm learns the spectral variability dictionary while simultaneously estimating abundance maps. This is achieved using a low-coherence dictionary learning problem to ensure spectral variability is distinct from endmember signatures.
3. Algorithmic Implementation: The optimization approach is driven by the Alternating Direction Method of Multipliers (ADMM), ensuring efficient handling of the resulting non-convex optimization problem.

Numerical Evaluation

The paper offers extensive experiments on both synthetic and real datasets. Key findings include:

• Synthetic Data: The ALMM significantly outperforms baseline methods including FCLSU, CLSU, and SUnSAL in terms of abundance estimation accuracy, as evidenced by reduced reconstruction errors and a higher correlation with ground truth abundance maps.
• Urban and Cuprite Scenes: The ALMM demonstrates superior accuracy by reducing spectral variability impacts, thereby producing clearer and more accurate abundance maps compared to PLMM and ELMM.

Implications and Future Directions

The introduction of the spectral variability dictionary enriches hyperspectral unmixing by allowing for a detailed decomposition of spectral signatures into endmember-related and variability-related components. This advancement not only enhances the robustness of unmixing algorithms to spectral variability but also opens avenues for integrating supervision in the learning process.

The paper suggests potential enhancements by exploring deeper learning methods within this framework, fostering more adaptive and responsive models to account for complex environmental interactions. Moreover, expanding the approach to other forms of spectral data and including domain-specific knowledge could further enhance its applicability.

Overall, the ALMM serves as a substantial contribution to hyperspectral unmixing by offering a refined modeling strategy that robustly addresses the pervasive challenge of spectral variability, marking a step forward in remote sensing technology and data analysis.