Estimating the Statistical Characteristics of Remote Sensing Big Data in the Wavelet Transform Domain

Since it is difficult to deal with big data using traditional models and algorithms, predicting and estimating the characteristics of big data is very important. Remote sensing big data consist of many large-scale images that are extremely complex in terms of their structural, spectral, and textual features. Based on multiresolution analysis theory, most of the natural images are sparse and have obvious clustering and persistence characters when they are transformed into another domain by a group of basic special functions. In this paper, we use a wavelet transform to represent remote sensing big data that are large scale in the space domain, correlated in the spectral domain, and continuous in the time domain. We decompose the big data set into approximate multiscale detail coefficients based on a wavelet transform. In order to determine whether the density function of wavelet coefficients in a big data set are peaky at zero and have a heavy tailed shape, a two-component Gaussian mixture model (GMM) is employed. For the first time, we use the expectation-maximization likelihood method to estimate the model parameters for the remote sensing big data set in the wavelet domain. The variance of the GMM with changing of bands, time, and scale are comprehensively analyzed. The statistical characteristics of different textures are also compared. We find that the cluster characteristics of the wavelet coefficients are still obvious in the remote sensing big data set for different bands and different scales. However, it is not always precise when we model the long-term sequence data set using the GMM. We also found that the scale features of different textures for the big data set are obviously reflected in the probability density function and GMM parameters of the wavelet coefficients.