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Differentiable sparse unmixing based on Bregman divergence for hyperspectral remote sensing imagery

Sparse unmixing has been successfully applied to hyperspectral remote sensing imagery based on the assumption that the observed image signatures can be expressed in a linear sparse regression with a large standard spectral library. Prior work for sparse unmixing usually utilizes L1 norm or Laplacian distribution to promote sparsity. Unfortunately, the L1 norm is not differentiable, which may lead to unstable results. In this paper, we adopt Bregman divergence for sparse unmixing, which is a differentiable, smoother prior. Based on the Maximum A Posterior (MAP) estimation, the proposed method has achieved sparse, stable and precise fractional abundances. The experimental results both simulated dataset and the real hyperspectral image demonstrate the effectiveness of the proposed differentiable sparse unmixing algorithm.