Innovation Modelling and Wavelet Analysis of Fractal Processes in Bio-Imaging

P.D. Tafti, D. Van De Ville, M. Unser

Proceedings of the Fifth IEEE International Symposium on Biomedical Imaging: From Nano to Macro (ISBI'08), Paris, France, May 14-17, 2008, pp. 1501-1504.

Growth and form in biology are often associated with some level of fractality. Fractal characteristics have also been noted in a number of imaging modalities. These observations make fractal modelling relevant in the context of bio-imaging.

In this paper, we introduce a simple and yet rigorous innovation model for multi-dimensional fractional Brownian motion (fBm) and provide the computational tools for the analysis of such processes in a multi-resolution framework. The key point is that these processes can be whitened by application of the appropriate fractional Laplacian operator which has a corresponding polyharmonic wavelet. We examine the case of MRI and mammography images through comparison with theoretical results, which underline the suitability of fractal models in the study of bio-textures.

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