Hyperspectral unmixing (HU) has become an important technique in exploiting hyperspectral data since it decomposes a mixed pixel into a collection of endmember spectra 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 Kurtosisbased 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. The proposed algorithm manages to outperform state of the art NMF-based algorithms in terms of extracting endmember spectra from hyperspectral data; therefore, it could uplift the performance of recent deep learning HU methods which utilizes the endmember spectra as supervisory input data for abundance extraction.

As field surveys used for manual lithological mapping are costly and time-consuming, digital lithological mapping (DLM) that utilizes remotely sensed spectral imaging provides a viable and economical alternative. Generally, DLM has been performed using spectral imaging with the use of laboratory-generated generic endmember signatures. However, the use of generic signatures is error-prone due to the presence of site-specific impurification processes. To that end, this paper proposes generating a single-target abundance mineral map for DLM, where the generated map can further be used as a guide for the selection or avoidance of a field survey. For that, a stochastic cancellation-based methodology was used to generate a site-specific endemic signature for the mineral in concern to reduce the inclusive nature otherwise present in DLM. Here, single-target detection allows the generation of a more accurate site-specific signature for lithological mapping as opposed to multi-target detection. Furthermore, a soil pixel alignment strategy to visualize the relative purity level of the target mineral has been introduced in the proposed work. Then, for the method validation, mapping of limestone deposits in the Jaffna peninsula of Sri Lanka was conducted as the case study using satellite-based spectral imaging as the input. It was observed that despite the low signal-to-noise ratio of the input hyperspectral data the proposed methodology was able to robustly extract the rich information contained in the input data. Further, a field survey was conducted to collect soil samples of four sites chosen by the proposed DLM from the Jaffna peninsula as an algorithm validation and to demonstrate the application of the proposed solution. The proposed abundance threshold of 0.1 -a hard decision boundary for limestone presence and absence -coincided with the industrial standard X-ray diffraction (XRD) threshold of 5 % for the mineral presence. The results of the XRD test validated the use of the algorithm in the selection of sites to be surveyed, hence could avoid conducting a costly field survey on the assumption of the existence of a mineral. Then a more rigorous survey may be performed, if required, only if the proposed digital lithological survey affirms.