Unser, MichaelMichaelUnserHorbelt, StefanStefanHorbeltTHIERRY BLU2024-03-082024-03-082000-03-3122195491https://scholars.lib.ntu.edu.tw/handle/123456789/640683We 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.conference paper2-s2.0-84937064865https://api.elsevier.com/content/abstract/scopus_id/84937064865