Toward a Sparse Bayesian Markov Random Field Approach to Hyperspectral Unmixing and Classification

Area of Science:

• Remote Sensing
• Computational Imaging
• Statistical Modeling

Background:

• Existing Bayesian hyperspectral unmixing algorithms benefit from Markov random fields for spatial correlations.
• Previous methods assumed stochastic abundance vectors, limiting performance.

Purpose of the Study:

• To propose a new Bayesian approach for joint hyperspectral unmixing and image classification.
• To relax the assumption of stochastic abundance vectors by using a common abundance vector for pixels within each class.
• To improve the speed and accuracy of hyperspectral data analysis.

Main Methods:

• A novel Bayesian model is formulated with a common abundance vector per class, utilizing a symmetric Dirichlet distribution.
• Inference is performed using a hybrid Gibbs sampler, incorporating simulated annealing for label estimation to prevent local optima.
• The model avoids stochastic reparameterizations inherent in previous methods.

Main Results:

• The proposed model demonstrates superior quantitative and qualitative performance compared to existing approaches on both synthetic and real hyperspectral datasets.
• Experiments show the new method is faster than current algorithms.
• The model's ability to induce sparsity in abundance vectors enhances robustness against overestimation of endmembers.

Conclusions:

• The developed Bayesian approach offers a significant advancement in joint hyperspectral unmixing and image classification.
• The method provides improved accuracy, speed, and robustness, particularly when dealing with complex spectral data.
• The flexibility of the Dirichlet distribution parameters allows for control over abundance vector sparsity, aiding in challenging unmixing scenarios.