  Hyperspectral unmixing (HU) has become an important technique in exploiting
hyperspectral data since it decomposes a mixed pixel into a collection of
endmembers weighted by fractional abundances. The endmembers of a hyperspectral
image (HSI) are more likely to be generated by independent sources and be mixed
in a macroscopic degree before arriving at the sensor element of the imaging
spectrometer as mixed spectra. Over the past few decades, many attempts have
focused on imposing auxiliary constraints on the conventional nonnegative
matrix factorization (NMF) framework in order to effectively unmix these mixed
spectra. As a promising step toward finding an optimum constraint to extract
endmembers, this paper presents a novel blind HU algorithm, referred to as
Kurtosis-based Smooth Nonnegative Matrix Factorization (KbSNMF) which
incorporates a novel constraint based on the statistical independence of the
probability density functions of endmember spectra. Imposing this constraint on
the conventional NMF framework promotes the extraction of independent
endmembers while further enhancing the parts-based representation of data.
Experiments conducted on diverse synthetic HSI datasets (with numerous numbers
of endmembers, spectral bands, pixels, and noise levels) and three standard
real HSI datasets demonstrate the validity of the proposed KbSNMF algorithm
compared to several state-of-the-art NMF-based HU baselines. The proposed
algorithm exhibits superior performance especially in terms of extracting
endmember spectra from hyperspectral data; therefore, it could uplift the
performance of recent deep learning HU methods which utilize the endmember
spectra as supervisory input data for abundance extraction.
