Fractal-based methods in analysis and signal image processing

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Fractal-based approximation methods take advantage of mathematical self-similarity in the object being analyzed. Finding such self-similarity in a digital signals/images facilitates the construction of fractal-based algorithms for image operations such as compression and denoising.  Such operations are of great concern when images are transmitted over a computer or cell phone connection, for example.  A very recent advancement involves the construction of "orbital pictures" via fractal-based techniques.  A simple example of an orbital picture is a field of corn or flowers disappearing off to the horizon.  Besides allowing for such images to be rendered with remarkable speed on a computer, there are other applications of these ideas to image representation. Finding such self-similarity in experimentally observed data can enable us to approximate the values of parameters in the mathematical model of the phenomenon being studied.  If the mathematical model is unknown, we may be able to determine its form.  Scientific research in a wide range of areas requires efficient model identification and parameter estimation techniques.