A novel l1/2 sparse regression method for hyperspectral unmixing
2013
Sun, Le | Wu, Zebin | Xiao, Liang | Liu, Jianjun | Wei, Zhihui | Dang, Fuxing
Hyperspectral unmixing (HU) is a popular tool in remotely sensed hyperspectral data interpretation, and it is used to estimate the number of reference spectra (end-members), their spectral signatures, and their fractional abundances. However, it can also be assumed that the observed image signatures can be expressed in the form of linear combinations of a large number of pure spectral signatures known in advance (e.g. spectra collected on the ground by a field spectro-radiometer, called a spectral library). Under this assumption, the solution of the fractional abundances of each spectrum can be seen as sparse, and the HU problem can be modelled as a constrained sparse regression (CSR) problem used to compute the fractional abundances in a sparse (i.e. with a small number of terms) linear mixture of spectra, selected from large libraries. In this article, we use the l₁/₂ regularizer with the properties of unbiasedness and sparsity to enforce the sparsity of the fractional abundances instead of the l₀ and l₁ regularizers in CSR unmixing models, as the l₁/₂ regularizer is much easier to be solved than the l₀ regularizer and has stronger sparsity than the l₁ regularizer (Xu et al. 2010). A reweighted iterative algorithm is introduced to convert the l₁/₂ problem into the l₁ problem; we then use the Split Bregman iterative algorithm to solve this reweighted l₁ problem by a linear transformation. The experiments on simulated and real data both show that the l₁/₂ regularized sparse regression method is effective and accurate on linear hyperspectral unmixing.
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