In this project we have implemented a linear denoising algorithm based on Duchon's smoothing formulation. Our algorithm is designed to denoise fractal-like signals, which are characterized by a power spectral density behavior as O(1 / ||w||^t). Since natural images approximate this kind of behavior, this algorithm can be applied to a wide range of images. An important application can be the denoising of biomedical imaging such as functional magnetic resonance imaging (fMRI), which have a fractal-like behavior. A very important characteristic of our denoising algorithm is that it gives the optimal discretization of the Wiener filter, which is the best linear technique.

We have implemented this algorithm as an ImageJ Plug-in. We use fractional polyharmonic B-splines as the basis of our implementation. The smoothing is performed by filtering in the Fourier domain. We have also implemented a demonstration applet: http://bigwww.epfl.ch/demo/fractaldenoising/.