Fractal-based modeling and interpolation of non-Gaussian images

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Abstract
In modeling terrain images corresponding to infrared scenes it has been found the images are characterized by a long-range dependence structure and high variability. The long-range dependence manifests itself in a `1/f' type behavior in the power spectral density and statistical self-similarity, both of which suggest the use of a stochastic fractal model. The traditional stochastic fractal model is fractional Brownian motion, which assumes the increment process arises from a Gaussian distribution. This model has been found to be rather limiting due to this restriction and therefore is incapable of modeling processes possessing high variability and emanating from long-tailed non-Gaussian distributions. Stable distributions have been shown to be good models of such behavior and have been incorporated into the stochastic fractal model, resulting in the fractional Levy stable motion model. The model is demonstrated on a terrain image and is used in an interpolation scheme to improve the resolution of the image.

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