Sobolev error estimates for filtered back projection reconstructions

Link:
Autor/in:
Verlag/Körperschaft:
IEEE
Erscheinungsjahr:
2017
Medientyp:
Text
Schlagworte:
  • Computerized tomography
  • Tomography
  • Limited view
  • Neutrons
  • Neutron Sources
  • Neutron Scattering
  • Computerized tomography
  • Tomography
  • Limited view
  • Neutrons
  • Neutron Sources
  • Neutron Scattering
Beschreibung:
  • This paper concerns the approximation of bivariate functions using the filtered back projection (FBP) formula from computerized tomography. To this end, we prove error estimates and convergence rates for the FBP reconstruction method for target functions f from a Sobolev space Hα(ℝ2) of fractional order α > 0, where we bound the FBP reconstruction error with respect to the (weaker) norms of the (rougher) Sobolev spaces Hσ(ℝ2), for 0 ≤ σ ≤ α. The results of this paper generalize previous of our findings in [2]-[4] for L2-error estimates, i.e., for the case σ = 0, to Sobolev error estimates for all fractional orders σ ϵ [0, α] and provide criteria to assess the performance of the utilized low-pass filter by means of its window function.
Lizenz:
  • info:eu-repo/semantics/closedAccess
Quellsystem:
Forschungsinformationssystem der UHH

Interne Metadaten
Quelldatensatz
oai:www.edit.fis.uni-hamburg.de:publications/1438312c-7ebb-4b68-a08d-80d7cead12cd