BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

Fractional Derivatives, Splines and Tomography

M. Unser, S. Horbelt, T. Blu

Proceedings of the Tenth European Signal Processing Conference (EUSIPCO'00), Tampere, Republic of Finland, September 4-8, 2000, vol. IV, pp. 2017–2020.

We develop a spline calculus for dealing with fractional derivatives. After a brief review of fractional splines, we present the main formulas for computing the fractional derivatives of the underlying basis functions. In particular, we show that the γth fractional derivative of a B-spline of degree α (not necessarily integer) is given by the γth fractional difference of a B-spline of degree α-γ. We use these results to derive an improved version the filtered backprojection algorithm for tomographic reconstruction. The projection data is first interpolated with splines; the continuous model is then used explicitly for an exact implementation of the filtering and backprojection steps. 

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AUTHOR="Unser, M. and Horbelt, S. and Blu, T.",
TITLE="Fractional Derivatives, Splines and Tomography",
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