Constrained Nonnegative Matrix Factorization for Blind Hyperspectral Unmixing incorporating Endmember Independence
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Hyperspectral image (HSI) analysis has become a key area in the field of remote sensing as a result of its ability to exploit richer information in the form of multiple spectral bands. The study of hyperspectral unmixing (HU) is important in HSI analysis due to the insufficient spatial resolution of customary imaging spectrometers. The endmembers of an 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. Signifying a step forward 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 endmembers. Imposing this constraint on the conventional NMF framework promotes the extraction of independent endmembers while further enhancing the parts-based representation of data. The proposed algorithm manages to outperform several state of the art NMF-based algorithms in terms of extracting endmembers from hyperspectral remote sensing data, hence could uplift the performance of recent deep learning HU methods which utilizes the endmembers as supervisory data for abundance extraction. Keywords: Hyperspectral unmixing (HU), blind source separation, kurtosis, constrained, Gaussianity, endmember independence, nonnegative matrix factorization (NMF).
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