Abstract
AbstractThe filtered back projection (FBP) formula allows us to reconstruct bivariate functions from given Radon samples. However, the FBP formula is numerically unstable and low‐pass filters with finite bandwidth and a compactly supported window function are employed to make the reconstruction by FBP less sensitive to noise. In this paper we analyse the inherent reconstruction error which is incurred by the application of a low‐pass filter with finite bandwidth. We present L2‐error estimates on Sobolev spaces of fractional order along with asymptotic convergence rates, where the filter's bandwidth goes to infinity. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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