Spectral Unmixing Model Based on Non-negative Matrix Factorization with Spatial and Spectral Correlation Constraints

Spectral un mixing has been an important technique for hyperspectral imagery processing. In spectral unmixing methods that are based on the original non-negative matrix factorization (NMF) model, unmixing accuracy is limited by the lack of appropriate constraints that derived from the inherent properties of hyperspectral images. It was shown that the correlation analysis can be extended for NMF-based spectral unmixing model, based on the advantage that the spatial and spectral correlation features can provide necessary constraints for NMF to overcome related problems and obtain better performance. However, many correlation constrained NMF models prefer adopting only spatial correlation, the neglect of spectral correlation may limit the accuracy and application scope. This letter presents a novel method of imposing spatial and spectral correlation constraints simultaneously on the NMF-based unmixing model by adopting Markov Random Field (MRF) and complexity pursuit respectively. The related issues, including reducing the deviation of endmembers' spatial energy distribution and substituting the predictability of signal for piecewise smoothness of spectra, were studied together. Experiments showed that the new proposed NMF model was superior to some existing NMF models with only spatial correlation constraint in terms of estimation accuracy of endmember spectra and fractional abundances.