DocumentCode :
696653
Title :
Fractional derivatives, splines and tomography
Author :
Unser, Michael ; Horbelt, Stefan ; Blu, Thierry
Author_Institution :
Biomedicai Imaging Group, Swiss Federal Institute of Technology Lausanne, CH-1015 Lausanne EPFL, Switzerland
fYear :
2000
fDate :
4-8 Sept. 2000
Firstpage :
1
Lastpage :
4
Abstract :
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 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.
Keywords :
Digital filters; Filtering algorithms; Image reconstruction; Polynomials; Splines (mathematics); Standards; Tomography;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Signal Processing Conference, 2000 10th European
Conference_Location :
Tampere, Finland
Print_ISBN :
978-952-1504-43-3
Type :
conf
Filename :
7075274
Link To Document :
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