Nonlinear unmixing of minerals based on the log and continuum removal model

Spectral mixing models for minerals can be complex, and choosing the right unmixing model is indispensable to ensure the accuracy of spectral unmixing. Continuum removal (CR) and natural log operation have the potential to eliminate nonlinear effects in spectral mixing, and have already been used in nonlinear spectral unmixing applications. In this study, the newly proposed log and CR (LCR) model and four other spectral unmixing models for mineral analysis (the linear model, CR model, natural log model, and simplified Hapke model) were summarized and applied to both laboratory mineral powder spectra and hyperspectral data of Cuprite, Nevada, USA. This paper summarizes the concept of mixing reflectance reconstruction (MRR), along with a comprehensive method to determine accuracy based on MRR results, which can be performed in different dimensions, such as spatial dimension and spectral dimension. The LCR model performed the best in both laboratory experiments and image data analysis, indicating its strong potential for practical application. The level of atmospheric correction's influence on unmixing accuracy varied for different spectral unmixing models, among which LCR model also had the best performance.