Tentative Study on Theory and Application of Remote Sensing Statistical Inference

We propose a new qualitative-quantitative remote sensing analytical method, remote sensing statistical inference, which is different from the remote sensing classification (qualitative analysis) and remote sensing inversion (quantitative analysis). Theoretically based on statistical optics and probability distribution transformation, remote sensing statistical inference mainly studies how the probability distributions of the ground parameters (e. g., soil moisture and temperature, water salinity and chlorophyll concentration, etc.) within the interested area change and affect the probability distributions (called spectral probability distribution, SPD) of the optical parameters (e. g., surface reflectance, remote sensing reflectance of water bodies, etc.) observed by the remote sensors, and how to infer the statistical distributions of the ground parameters in this region based on the SPDs observed by the sensor, to provide the corresponding qualitative and quantitative information for characterizing the ground parameters. Compared with the traditional remote sensing classification and inversion, the advantages of remote sensing statistical inference are: (1) it can quickly obtain the global statistical characteristics of the ground parameters, such as mean, variance, max/min, etc., without inversion of each image pixels, which is especially important for many current remote sensing applications based on big data and high-resolution images, because some application department managers are most interested in the overall statistical distributions of the management objects (such as lakes and reservoirs); (2) the observed SPDs can be directly used in the classification study of ground objects, providing a new classification method different from the traditional remote sensing classification based on the signature features of each pixel, which provides the overall classification of the study object (such as the classification of a lake) rather than the classification of each pixel (e. g., the classification of water quality); (3) remote sensing statistical inference can provide auxiliary information for remote sensing inversion modeling, and based on the inferred information, the functions and/or parameters of inversion modelscan be adjusted so that the statistical characteristics of the inversed results match the inferred results. This paper briefly introduces some basic concepts and principles of remote sensing statistical inference, its advantages over remote sensing classification and inversion, the applicable objects of inference and remote sensing data processing methods for inference, analyzes the characteristics of the spectral probability distribution of major lakes in China, and proposes a bootstrap-based method for inference using the field measurement data of West Lake in Hangzhou. A simple inference method based on the bootstrap-based method is proposed to infer the key statistical distribution parameters, for example, the mean concentration of the suspended particles in West Lake.