Investigation of nonlinearity in hyperspectral remotely sensed imagery — a nonlinear time series analysis approach

Hyperspectral remotely sensed imagery is often modeled and processed by algorithms assuming that the imagery is a realization of a Gaussian linear stochastic process. These algorithms include some methods for feature extraction, spectral mixture analysis, and spatial analysis. The linear assumption, however, may not be realistic since there are factors that may introduce nonlinearities during the formulation of hyperspectral imagery. The existence of nonlinearity has a negative impact on the effectiveness and accuracy of information extraction. In this study, we propose a method to investigate the existence of nonlinearity in hyperspectral data, represented by a 4m AVIRIS image acquired over an area of coastal forests on Vancouver Island. The proposed method is based on a statistical test using surrogate data, an approach originally introduced in nonlinear time series analysis. High-order autocorrelations are used as the discriminating statistic to evaluate the differences between the hyperspectral data and their surrogates. Instead of conducting a statistical test in time domain as is used in typical time series analysis, we did it in spatial and spectral domains. The investigation revealed that the existence of nonlinearity in hyperspectral data is evident in spectral domain, but not in the spatial domain.