Research on the Hyperspectral-based Unmixing Model of Composite Pigments on Mural Surfaces

Abstract. Murals constitute an invaluable component of cultural heritage, encapsulating profound artistic and historical significance. Hyperspectral remote sensing, as a non-destructive testing technique, offers an effective means for analysing and identifying mural pigments. We proposed a spectral unmixing method based on the negative logarithm of spectral reflectance, aimed at improving the accuracy of quantitative analysis for composite pigments in murals. We obtained three sets of mixed spectra: cinnabar-orpiment, azurite-orpiment, and azurite-malachite. The original reflectance was converted into negative logarithmic values, and linear models were applied for unmixing. Supervised unmixing was conducted in the experiment to evaluate the model’s precision, with the unmixing process carried out using known endmembers. The unmixing accuracy was quantified using the Root Mean Square Error, which compares the estimated abundances of all endmembers with actual values. Additionally, a comparison was made between the negative logarithmic transformation and the commonly used transformations of original reflectance, first derivative, and second derivative. The result show that the logarithmic hyperspace linear model simplifies spectral unmixing complexity, enhancing the accuracy of linear unmixing models in addressing mixed pigment unmixing problems. To validate the effectiveness of the proposed method for real murals, the improved model was applied to the hyperspectral data unmixing analysis of murals collected by the Yungang Academy, located in Shanxi Province, China. Experimental findings demonstrate that, compared to traditional methods, the improved unmixing approach more precisely represents the pigment distribution in the murals. This study offers new ideas and methods for the digital preservation and restoration of mural composite pigments.