A spatial compositional model for linear unmixing and endmember uncertainty estimation

Area of Science:

• Remote Sensing
• Signal Processing
• Geospatial Analysis

Background:

• The normal compositional model (NCM) is widely used for hyperspectral unmixing but assumes pixel independence.
• This assumption is often violated, leading to endmember uncertainty, which affects unmixing accuracy.

Purpose of the Study:

• To develop a novel hyperspectral unmixing model that addresses the limitations of the NCM.
• To introduce the spatial compositional model (SCM) that accounts for pixel dependencies and spatial information.

Main Methods:

• Derived the SCM from first principles without the pixel independence assumption.
• Incorporated wavelength-dependent noise levels and spatial-sparsity priors for abundances.
• Utilized projected gradient descent to solve the maximum a posteriori objective for simultaneous estimation.

Main Results:

• SCM demonstrated superior performance compared to state-of-the-art algorithms on synthetic and real hyperspectral data.
• The model accurately estimates endmembers, abundances, noise variances, and endmember uncertainty.
• Estimated uncertainty provides a reliable predictor of endmember error.

Conclusions:

• The SCM offers a more robust and accurate approach to hyperspectral unmixing.
• Accounting for spatial information and endmember uncertainty significantly improves unmixing results.
• SCM provides valuable insights into the reliability of estimated endmembers.