Hyperspectral Unmixing Based on Weighted L1/2 Regularization

Sparse unmixing is based on the assumption that each mixed pixel in the hyperspectral image can be expressed in the form of linear combinations of a number of pure spectral signatures that are known in advance. Despite the success of sparse unmixing based on the L
₀
or L
₁
regularizer, the limitation of this approach on its computational complexity or sparsity affects the efficiency and accuracy. In this paper, we choose the L
_1/2
norm as an alternative regularizer which is much easier to solved than L
₀
regularizer and has better sparsity and robustness than L
₁
regularizer. We proposed a weighted L
_1/2
sparsity regularized unconvex variation model for the hyperspectral unmixing, namely WL
_1/2
SU model. The unconvex optimization problem was simply transformed into a series of re-weighted L
₁
regularization problems, and use the variable splitting and augmented Lagrangian algorithm to solve it. Our experimental results with simulated data sets and real hyperspectral data sets demonstrate that the proposed WL
_1/2
SU method is an effective and simple spectral unmixing algorithm for hyperspectral unmixing.