Using image pyramids for the acceleration of spectral unmixing based on nonnegative matrix factorization

In the last couple of years, methods based on nonnegative matrix factorization (NMF) have been used for spectral unmixing of hyperspectral images. We propose a meta-method based on image pyramids for the acceleration of the unmixing calculation. Starting the factorization from a spatially coarse level, neighboring pixel spectra are averaged and considered as new pixel spectra. In the subsequent iterations, the resolution is increased step by step, which means that the previous lower resolution outcomes can be regarded as close-to-optimal starting points for the higher resolution iterations. By performing many steps on lower resolution levels, only few steps have to be calculated on the original size data. We will demonstrate the application of the new method, showing that for both spatial and spectral extensions of NMF, the proposed method in most cases leads to equal objective function values in less time. The unmixing calculation can be accelerated up to several times. Due to the fact that the objective functions of different NMF algorithms exhibit more or less local minima, not all NMF-based unmixing algorithms are equally well-suited for the application of the proposed method.