EPFL | Biomedical Imaging Group | Fractional Splines

The Fractional Spline Wavelet Transform: Definition and Implementation

T. Blu, M. Unser

Proceedings of the Twenty-Fifth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'00), Istanbul, Turkey, June 5-9, 2000, vol. I, pp. 512–515.

We define a new wavelet transform that is based on a recently defined family of scaling functions: the fractional B-splines. The interest of this family is that they interpolate between the integer degrees of polynomial B-splines and that they allow a fractional order of approximation.

The orthogonal fractional spline wavelets essentially behave as a fractional differentiators. This property seems promising for the analysis of 1/f^α; noise that can be whitened by an appropriate choice of the degree of the spline transform.

We present a practical FFT-based algorithm for the implementation of these fractional wavelet transforms, and give some examples of processing.

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