Sparse hyperspectral unmixing based on smoothed ℓ0 regularization

• This paper present a new sparse hyperspectral unmixing method based on smoothed ℓ0 norm.
• The smoothed ℓ0 norm is a continuous function, which provides a smooth measure of ℓ0 sparsity and better accuracy than ℓ1 norm and also tolerates noise to some extent.
• The experimental results show effectiveness and accuracy of the proposed method.

Sparse based approach has recently received much attention in hyperspectral unmixing area. Sparse unmixing is based on the assumption that each measured pixel in the hyperspectral image can be expressed by a number of pure spectra linear combination from a spectral library known in advance. Despite the success of sparse unmixing based on the ℓ0 or ℓ1 regularizer, the limitation of this approach on its computational complexity or sparsity affects the efficiency or accuracy. As the smoothed ℓ0 regularizer is much easier to solve than the ℓ0 regularizer and has stronger sparsity than the ℓ1 regularizer, in this paper, we choose the smoothed ℓ0 norm as an alternative regularizer and model the hyperspectral unmixing as a constrained smoothed ℓ0 − ℓ2 optimization problem, namely SL0SU algorithm. We then use the variable splitting augmented Lagrangian algorithm to solve it. Experimental results on both simulated and real hyperspectral data demonstrate that the proposed SL0SU is much more effective and accurate on hyperspectral unmixing than the state-of-the-art SUnSAL method.