Hyperspectral image non-linear unmixing using joint extrinsic and intrinsic priors with L1/2-norms to non-negative matrix factorisation

Hyperspectral unmixing (HU) is one of the most active emerging areas in image processing that estimates the hyperspectral image’s endmember and abundance. HU enhances the quality of both spectral and spatial dimensions of the image by modifying the endmember and abundance parameters of the hyperspectral images. There are several HU algorithms available in the literature based on the linear mixing model (LMM) that deals with the microscopic contents of the pixels in the images. Non-negative matrix factorisation (NMF) is the prominent method widely used in LMMs that simultaneously estimates both the endmembers and abundances parameters along with some residual factors of the image to improve the quality of unmixing. In addition to this, the quality of the image is enhanced by incorporating some constraints to both endmember and abundance matrices with the NMF method. However, all the existing methods apply any of these constraints to the endmember and abundance matrices by considering the linearity features of the images. In this paper, we propose an unmixing model called joint extrinsic and intrinsic priors with L1/2 norms to non-negative matrix factorisation (JEIp L1/2-NMF) that applies multiple constraints simultaneously to both endmember and abundance matrices of the hyperspectral image to enhance its quality. Three main external and internal constraints such as minimum volume, sparsity and total variation are applied to both the endmembers and abundance parameters of the image. In addition, a L1/2-norms is imposed to extract good quality spectral data. Therefore, the proposed method enhances spatial as well as spectral data and considers the non-linearity of the pixels in the image by adding a residual term to the model. Performance of our proposed model is measured by using different quality measuring indexes on four benchmark public datasets and found that the proposed method shows outstanding performance compared to all the conventional baseline methods. Further, we also evaluated the performance of our method by varying the number of endmembers empirically and concluded that less than five endmembers provides high-quality spectral and spatial data during the unmixing process.