Hyperspectral Sparse Unmixing Of Mixed Pigments Based On Nonlinear Model

The number of painted artifacts is numerous and the painted artifacts are characterized by rich colors,which are an important part of Chinese cultural heritage and have rich historical value and high scientific research value.The pigment on the surface of the painted artifacts is the main characteristics.However,due to the influence of human factors and natural factors,the color on surface of painted artifacts will appear to be lost or faded.Therefore,it is urgent to use modern scientific technology to provide help for color restoration.Traditional scientific methods will cause secondary irreversible damage to the painted artifacts and are usually local detection.Hyperspectral technology as a fast and nondestructive method has been widely concerned in recent years.According to painting techniques,painters often use a variety of pigments to mix.Therefore,the rich colors on the surface of painted artifacts are usually composed of a variety of pure pigments.With the development of hyperspectral imaging in the research of pigment,many scholars have introduced the idea of hyperspectral unmixing into the research of mixed pigment.Pure pigments are regarded as endmembers.Through the unmixing algorithm,the abundance map of pure pigments on the surface of painted artifacts is obtained.The map can provide scientific guidance for cultural heritage protection.However,most of the current research is based on linear mixing model,the model of the actual surface should be a more complex nonlinear mixing,and there is no pure endmember on the surface of cultural heritages,which leads to the error of endmember extraction.Based on the above problems,this paper has carried out a series of studies.First,for the pretreatment,this paper studies the intensity distribution of the ground hyperspectral light source used in cultural heritage protection,this paper proposes a reflectance calibration method based on surface fitting.Then,for the nonlinear mixed model,the Kubelk-Munk model and the Hapke model are studied,and an improved KM model is proposed.Last,for the problem that there is no pure endmember on the surface of painted artifacts,combined with the improved KM model,a sparse unmixing algorithm based on the improved KM model is proposed.The main research results are as follows:(1)A reflectance calibration method based on surface fitting is proposed.Firstly,the characteristics of light source distribution of hyperspectral imaging technology in cultural heritage protection are studied.It is found that it has the characteristics of uneven distribution.But the characteristics that light intensity distribution is not considered in traditional reflectance calibration.Based on this,a reflectance calibration method based on surface fitting is proposed.Then,two different fitting models are studied,and Gaussian surface is selected as the fitting model according to the experimental results.Finally,experiments on hyperspectral images of a homogeneous sample and a real mural show that the proposed method has higher accuracy than traditional reflectance calibration.(2)An improved KM model is proposed.Firstly,two commonly used spectral models,KM model and Hapke model,are studied.Then,according to the characteristics of traditional Chinese painted artifacts,the single constant KM model is improved.The cementitious material and substrate are introduced to calculate the abundance.Finally,through the experimental results of self-made mixed samples in the laboratory,it is found that the improved KM model has the highest accuracy in the three models,and the proposed model has higher unmixing accuracy than the linear model.The experimental results show that the improved model can effectively transform the nonlinear mixture into linear mixture,which can improve the accuracy of linear unmixing algorithm.(3)A sparse unmixing algorithm based on improved KM model is proposed.Different from other application fields of the unmixing algorithm,there are some unique characteristics in painted artifacts,which is no pure endmember on the surface.The reason is that the surface of painted artifacts only has mixed pigments.This characteristic leads to errors in the traditional unmixing process(endmember extraction and abundance solution).Based on this,the sparse unmixing algorithm is studied in this paper.The spectral library is regarded as the combination of endmembers,so as to avoid the step of endmember extraction.Then,because sparse unmixing algorithm is still linear,the accuracy of the unmixing of the nonlinear mixed pigments needs to be improved.Combining with the nonlinear model studied above,a sparse unmixing algorithm based on improved KM model is proposed.The reflectance is converted to absorption scattering ratio.Finally,the experiment is carried out on the samples made in the laboratory and a real mural to verify the effectiveness of the proposed method.