Sampling Theory and Parallel-Beam Tomography
- 490 Downloads
This article contains a tutorial on the interaction between sampling theory and tomography as well as some new results. We explore how sampling theorems are used in tomography to identify efficient data acquisition schemes, facilitate an error analysis for reconstruction algorithms, and provide a qualitative understanding of some image artifacts. In turn, applications in tomography have stimulated research on new estimates for the aliasing error and in non-uniform sampling theory. New results are included in an analysis of artifacts caused by undersampling.
KeywordsSampling Condition Reciprocal Lattice Sampling Theory Sampling Lattice Convolution Kernel
Unable to display preview. Download preview PDF.
- M. Abramowitz and I. A. StegunHandbook of Mathematical FunctionsU.S. Dept. of Commerce, Washington, DC, 1972.Google Scholar
- L. Desbat, Interpolation of lacking data in tomographyConference on Sampling Theory and Applications Proceedings of Samp T Intern. Proceedings of Samp T InternMay 2001Orlando, FL, pp. 123–128,2001.Google Scholar
- A. Faridani, Reconstructing from efficiently sampled data in parallel-beam computed tomographyInverse Problems and ImagingG. F. Roach (ed.), Pitman Research Notes in Mathematics Series, Vol. 245, Longman, 1991, pp. 68–102.Google Scholar
- A. Faridani, Sampling in parallel-beam tomography, Inverse Problems, Tomography, and Image Processing, A. G. Ramm (editor), Plenum, New York, 1998, pp. 33–53.Google Scholar
- F. Natterer, Recent developments in x-ray tomographyTomography, Impedance Imaging, and Integral GeometryE. T; Quinto, M. Cheney, and P. Kuchment (eds.), Lectures in Applied Mathematics, Vol. 30, Amer. Math. Soc, Providence, RI, 1994, pp. 177–198.Google Scholar
- F. Natterer, Resolution and reconstruction for a helical CT scannerTechnical Report 20/96-NMathematics Dept., University of Münster, Germany.Google Scholar
- S. W. Rowland, Computer implementation of image reconstruction formulas, Image Reconstruction from Projections: Implementation and Applications, G. T. Herman (ed.), Springer, Berlin, 1979.Google Scholar