Algorithm and code for analyzing hyperspectral images using the Hurst exponent

Abstract

The main goal of this paper is to present the implementation of an algorithm developed to calculate the Hurst exponent (H), applied here to characterize the pixel spectrum from hyperspectral image. Because a hyperspectral reflectance curve from each pixel may be regarded as a chaotic series that fact inspires us to treat a spectrum as a time series. Hyperspectral data are typical heteroscedastic variables, which makes it inappropriate to apply the normal/classic time series analysis, such as the autoregressive-integrated-moving-average model. Generally, the Hurst exponent is a measure used in nonlinear time series analysis to reveal local trend of series among adjacent successive terms. H can describe the local change in the ratio between the ranges of accumulated mean-removed values to the original standard deviation and thus represents the diversity of spectral values. Although H may be used to characterize regions of the image regarding persistence or antipersistence spectrum (highlighting noisy data), it does not directly address the separation between the classes of interest. The algorithm uses the rescaled range analysis method. This method introduces a measure of the variability of a time series using a ratio range/standard deviation (R/S). The algorithm was tested on hyperspectral data with spectra of various lengths and with persistence or antipersistence spectrum.

Keywords

• hyperspectral data
• spectral profiles
• time series
• Hurst exponent
• persistent spectrum