Bilateral filter based total variation regularization for sparse hyperspectral image unmixing

Abstract

Spectral unmixing of hyperspectral images aims to find the proportion of constituent materials in mixed pixels. The total variation (TV) regularization is widely included in classical sparse regression formulations to exploit the spatial information in hyperspectral data. It promotes piecewise constant transitions in the fractional abundance of the same endmember among neighboring pixels. The TV regularization term, however, usually brings some staircase effects. To alleviate this drawback, we propose a bilateral filter based TV regularization for hyperspectral image unmixing. Then we present an unmixing model that combines a data-fidelity term, a sparsity regularization term, and the new regularization term. To solve the proposed model, we design an algorithm called sparse unmixing via variable splitting augmented Lagrangian and bilateral filter based TV (SUnSAL-BF-TV), under the alternating direction method of multipliers (ADMM) framework. Our experimental results show that our algorithm is effective to unmix both simulated and real hyperspectral data sets.