INFRARED SCENE MODELING AND INTERPOLATION USING FRACTIONAL LÉVY STABLE MOTION

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Abstract
Many data arising from natural phenomena exhibit "1/f" behavior, indicating a long-range dependence structure in the increments. The data is said to be self-similar or fractal, which has been traditionally modeled by fractional Brownian motion (fBm). This stochastic fractal model assumes a Gaussian distribution of the increments which is at times too rigid, particularly for data emanating from a long-tailed distribution. Therefore, the fractional Lévy stable motion stochastic process is proposed as a means of modeling a wider range of data. For these processes the increments are assumed to be from the family of stable distributions which have been shown to be good models of long-tailed behavior. The model is applied to data from infrared scenes and used to perform fractal interpolation, preserving not only the self-similarity, but also the probability distribution of the increments over the newly generated scales. This offers a flexible new model for a broader class of data than the fBm model.

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