The approximate inverse in action II: Convergence and stability

Mathematics of Computation

Volumn 72, Issue 243, 2003, Pages 1399-1415

  Rieder, Andreas ^a   Schuster, Thomas ^b  

^a UNIVERSITY OF KARLSRUHE   (Germany)

^b SAARLAND UNIVERSITY   (Germany)

Author keywords

Approximate inverse; Filtered backprojection; Mollification; Radon transform

Indexed keywords

EID: 0038468561     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-03-01526-6     Document Type: Article

References (17)

1. J. H. BRAMBLE AND S. R. HILBERT, Estimation of linear functional on Sobolev spaces with application to Fourier transforms and spline interpolation, SIAM J. Numer. Anal., 7 (1970), pp. 112-124. MR 41:7819
2. A. COHEN, I. DAUBECHIES, AND J.-C. FEAUVEAU, Biorthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math., 45 (1992), pp. 485-560. MR 93e:42044
3. W. DAHMEN, A. KUNOTH, AND K. URBAN, Biorthogonal spline wavelets on the interval -stability and moment conditions, Appl. Comp. Harm. Anal., 6 (1999), pp. 132-196. MR 99m:42046
4. H. W. ENGL, M. HANKE, AND A. NEUBAUER, Regularization of Inverse Problems, vol. 375 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, 1996. MR 97k:65145
5. J. L. LIONS AND E. MAGENES, Non-Homogeneous Boundary Value Problems and Applications, Vol. 1, Springer-Verlag, New York, 1972. MR 50:2670
6. A. K. LOUIS, Inverse und schlecht gestellte Probleme, Studienbücher Mathematik, B. G. Teubner, Stuttgart, Germany, 1989. MR 90g:65075
7. _, Corrigendum: Approximate inverse for linear and some nonlinear problems, Inverse Problems, 12 (1996), pp. 175-190. MR 96m:65063
8. _, A unified approach to regularization methods for linear ill-posed problems, Inverse Problems, 15 (1999), pp. 489-498. MR 2000b:65111
9. A. K. LOUIS AND P. MAASS, A mollifier method for linear operator equations of the first kind, Inverse Problems, 6 (1990), pp. 427-440. MR 91g:65130
10. F. NATTERER, The Mathematics of Computerized Tomography, Wiley, Chichester, 1986. MR 88m:44008
11. P. OSWALD, Multilevel Finite Element Approximation: Theory and Applications, Teubner Skripten zur Numerik, B. G. Teubner, Stuttgart, Germany, 1994. MR 95k:65110
12. D. A. POPOV, On convergence of a class of algorithms for the inversion of the numerical Radon transform, in Mathematical Problems of Tomography, I. M. Gelfand and S. G. Gindikin, eds., vol. 81 of Translations of Mathematical Monographs, AMS, Providence, R.I., 1990, pp. 7-65. MR 92g:92010
13. A. RIEDER, Principles of reconstruction filter design in 2D-computerized tomography, in Radon Transforms and Tomography, T. Quinto, L. Ehrenpreis, A. Faridani, F. Gonzales, and E. Grinberg, eds., vol. 278 of Contemporary Mathematics, AMS, Providence, RI, 2001. MR 2002f:65188
14. A. RIEDER AND TH. SCHUSTER, The approximate inverse in action with an application to computerized tomography, SIAM J. Numer. Anal., 37 (2000), pp. 1909-1929. MR 2001a:65072
15. L. L. SCHUMAKER, Spline Functions: Basic Theory, Pure & Applied Mathematics, John Wiley & Sons, New York, 1981. MR 82j:41001
16. L. A. SHEPP AND B. F. LOGAN, The Fourier reconstruction of a head section, IEEE Trans. Nuc. Sci., 21 (1974), pp. 21-43.
17. J. WLOKA, Partial Differential Equations, Cambridge University Press, Cambridge, U. K., 1987. MR 88d:35004