Scale invariance and structured order exhibited by the statistics of remote-sensing imagery

Image intensity fields produced by remote sensing of the Earth from space have strongly non-Gaussian statistics, reflecting the existence of a high degree of structured order. The statistical description of such complex stochastic fields is substantially simplified by the phenomenon of scale invariance, associated with the fractal structures discussed by Mandelbrot. In this paper, typical properties of scale invariance and structured order are exhibited, using a statistical methodology which involves multi-resolution sampling and filtering. For comparison with remote-sensing data, results are also presented for an example of a strongly non-Gaussian computer-generated image related to the Mandelbrot set.