论文信息 - A singular value decomposition for the radon transform in n-dimensional euclidean space

A singular value decomposition for the radon transform in n-dimensional euclidean space

We construct the singular value decomposition of the Radon transform when the Radon transform is restricted to functions which are either square integrable on the unit disc in IR n with respect to one of the weights (1-r 2)n/2-λ: or square integrable on IR n with respect to exp(r 2). An application to calculating mollifiers for approximate inversion of the sampled Radon transform is discussed.

M. E. Davison

[1] G. Herman,et al. Three-dimensional reconstruction from projections: a review of algorithms. , 1974, International review of cytology.

[2] A. Cormack. Representation of a Function by Its Line Integrals, with Some Radiological Applications , 1963 .

[3] M. Nashed. Generalized Inverses and Applications: Proceedings of an Advanced Seminar , 1976 .

[4] R. Marr,et al. On Two Approaches to 3D Reconstruction in NMR Zeugmatography , 1981 .

[5] M. E. Davison,et al. Tomographic reconstruction with arbitrary directions , 1981 .

[6] R. A. Brooks,et al. Principles of computer assisted tomography (CAT) in radiographic and radioisotopic imaging , 1976, Physics in medicine and biology.

[7] M. Z. Nashed,et al. Annotated Bibliography on Generalized Inverses and Applications , 1976 .

[8] C. D. Maldonado,et al. New Method for Obtaining Emission Coefficients from Emitted Spectral Intensities. Part II—Asymmetrical Sources* , 1966 .