Spectral–Spatial Weighted Sparse Regression for Hyperspectral Image Unmixing
Spectral unmixing aims at estimating the fractional abundances of a set of pure spectral materials (endmembers) in each pixel of a hyperspectral image. The wide availability of large spectral libraries has fostered the role of sparse regression techniques in the task of characterizing mixed pixels in remotely sensed hyperspectral images. A general solution for sparse unmixing methods consists of using the  $\ell _{1}$  regularizer to control the sparsity, resulting in a very promising performance but also suffering from sensitivity to large and small sparse coefficients. A recent trend to address this issue is to introduce weighting factors to penalize the nonzero coefficients in the unmixing solution. While most methods for this purpose focus on analyzing the hyperspectral data by considering the pixels as independent entities, it is known that there exists a strong spatial correlation among features in hyperspectral images. This information can be naturally exploited in order to improve the representation of pixels in the scene. In order to take advantage of the spatial information for hyperspectral unmixing, in this paper, we develop a new spectral–spatial weighted sparse unmixing (S2WSU) framework, which uses both spectral and spatial weighting factors, further imposing sparsity on the solution. Our experimental results, conducted using both simulated and real hyperspectral data sets, illustrate the good potential of the proposed S2WSU, which can greatly improve the abundance estimation results when compared with other advanced spectral unmixing methods.