A modified SUnSAL-TV algorithm for hyperspectral unmixing based on spatial homogeneity analysis

The sparse regression framework has been introduced by many works to solve the linear spectral unmixing problem due to the knowledge that a pixel is usually mixed by less endmembers compared with the endmembers in spectral libraries or the entire hyperspectral data sets. Traditional sparse unmixing techniques focus on analyzing the spectral properties of hyperspectral imagery without incorporating spatial information. But the integration of spatial information would be beneficial to promote the performance of the linear unmixing process. An algorithm called sparse unmixing via variable splitting augmented Lagrangian and total variation (SUnSAL-TV) adds a total variation spatial regularizer besides the sparsity-inducing regularizer to the final unmixing objective function. The total variation spatial regularization is helpful to promote the fractional abundance smoothness. However, the abundance smoothness varies in the image. In this paper, the spatial smoothness is estimated through homogeneity analysis. Then the spatial regularizer is weighted for each pixel by a homogeneity index. The modified algorithm, called homogeneity analysis based SUnSAL-TV (SUnSAL-TVH), integrates the spatial information with finer modelling of spatial smoothness and is supposed insensitive to the noise and more stable. Experiments on synthetic data sets are taken and indicate the validity of our algorithm.