Fractional derivatives, splines and tomography

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 $ γ ^{ th } $ fractional derivative of a B-spline of degree α (not necessarily integer) is given by the $ γ ^{ th } $ 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.

Published in:
Proc. European Signal Processing Conference (EUSIPCO), 4, 2017-2020
Presented at:
Tenth European Signal Processing Conference (EUSIPCO'00), Tampere, Finland

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 Record created 2005-04-18, last modified 2020-10-25

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