Investigation of Nonlinearity in Hyperspectral Imagery Using Surrogate Data Methods

Although hyperspectral remotely sensed data are believed to be nonlinear, they are often modeled and processed by algorithms assuming that the data are realizations of some linear stochastic processes. This is likely due to the reason that either the nonlinearity of the data may not be strong enough, and the algorithms based on linear data assumption may still do the job, or the effective algorithms that are capable of dealing with nonlinear data are not widely available. The simplification on data characteristics, however, may compromise the effectiveness and accuracy of information extraction from hyperspectral imagery. In this paper, we are investigating the existence of non- linearity in hyperspectral data represented by a 4-m Airborne Visible/Infrared Imaging Spectrometer image acquired over an area of coastal forests on Vancouver Island. The method employed for the investigation is based on the statistical test using surrogate data, an approach often used in nonlinear time series analysis. In addition to the high-order autocorrelation, spectral angle is utilized as the discriminating statistic to evaluate the differences between the hyperspectral data and their surrogates. To facilitate the statistical test, simulated data sets are created under linear stochastic constraints. Both simulated and real hyperspectral data are rearranged into a set of spectral series where the spectral and spatial adjacency of the original data is maintained as much as possible. This paper reveals that the differences are statistically significant between the values of discriminating statistics derived from the hyperspectral data and their surrogates. This indicates that the selected hyperspectral data are nonlinear in the spectral domain. Algorithms that are capable of explicitly addressing the nonlinearity are needed for processing hyperspectral remotely sensed data.