A novel l 1/2 sparse regression method for hyperspectral unmixing
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 l
1/2 regularizer with the properties of unbiasedness and sparsity to enforce the sparsity of the fractional abundances instead of the l
0 and l
1 regularizers in CSR unmixing models, as the l
1/2 regularizer is
much easier to be solved than the l
0 regularizer and has stronger sparsity than the l
1 regularizer (Xu et al. 2010). A reweighted iterative algorithm is introduced to convert the l
1/2 problem into the l
1 problem; we
then use the Split Bregman iterative algorithm to solve this reweighted l
1 problem by a linear transformation. The experiments on simulated and real data both show that the l
1/2 regularized sparse regression method is effective and accurate on linear hyperspectral
unmixing.
Document Type: Research Article
Affiliations: 1: School of Computer Science and Technology, NJUST, Nanjing, China 2: Jiangsu Key Lab of Spectral Imaging and Intelligent Sensing, NJUST, Nanjing, China 3: Aero Geophysical Survey Remote Sensing Centre, Ministry of Land and Resources, Beijing, China
Publication date: 20 October 2013
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