Parameter selection methods for axisymmetric flame tomography through Tikhonov regularizaron

Applied Optics

Volumn 47, Issue 3, 2008, Pages 407-416

  Åkesson, Emil O ^a   Daun, Kyle J ^b,c  

^a LUND INSTITUTE OF TECHNOLOGY   (Sweden)

^b NATIONAL RESEARCH COUNCIL CANADA   (Canada)

^c UNIVERSITY OF WATERLOO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DECONVOLUTION; PARAMETER ESTIMATION; PROBLEM SOLVING;

AXISYMMETRIC FLAME TOMOGRAPHY; L-CURVE CURVATURE;

TOMOGRAPHY;

EID: 41549119442     PISSN: 1559128X     EISSN: 15394522     Source Type: Journal    
DOI: 10.1364/AO.47.000407     Document Type: Article

References (24)

1. C. J. Dasch, "One-dimensional tomography: a comparison of Abel, onion-peeling, and filtered backprojection methods," Appl. Opt. 31, 1146-1152 (1992).
2. R. J. Hall and P. A. Bonczyk, "Sooting flame thermometry using emission/absorption tomography," Appl. Opt. 29, 4590-4598 (1990).
3. D. R. Snelling, K. A. Thomson, G. J. Smallwood, and Ö. L. Guider, "Two-dimensional imaging of soot volume fraction in laminar diffusion flames," Appl. Opt. 38, 2478-2485 (1999).
4. F. Cignoli, S. De Luliis, V. Manta, and G. Zizak, "Two-dimensional two-wavelength emission technique for soot diagnostics," Appl. Opt. 40, 5370-5378 (2001).
5. R. Gorenflo and S. Vessella, Abel Integral Equations: Analysis and Applications (Springer, 1993).
6. J. P. Holloway, S. Shannon, S. M. Sepke, and M. L. Brake, "A reconstruction algorithm for a spatially resolved plasma optical emission spectroscopy sensor," J. Quant. Spectrosc. Radiat. Transfer 68, 101-115 (2001).
7. K. J. Daun, K. A. Thomson, F. Liu, and G. J. Smallwood, "Deconvolution of axisymmetric flame properties using Tikhonov regularization," Appl. Opt. 45, 4638-4646 (2006).
8. C. Wu, Department of Chemical Engineering, Tsinghua University, Beijing, China (personal communication, 2007).
9. A. N. Tikhonov and V. A. Arsenin, Solution of Ill-Posed Problems (Winston & Sons, 1977).
10. P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion (SIAM, 1998).
11. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 1992).
12. V. A. Morozov, "On the solution of functional equations by the method of regularization," Sov. Math. Dokl. 7, 414-417 (1966).
13. P. C. Hansen and D. P. O'Leary, "The use of the L-curve in the regularization of discrete ill-posed problems," SIAM J. Sci. Comput. (USA) 14, 1487-1503 (1993).
14. G. H. Golub, M. Heath, and G. Wahba, "Generalized cross-validation as a method for choosing a good ridge parameter," Technometrics 21, 215-223 (1979).
15. G. Wahba, Spline Models for Observational Data (SIAM, 1990).
16. J. Hadamard, Lectures on Cauchy's Problem in Linear Differential Equations (Yale U. Press, 1923).
17. W. S. Cleveland and S. J. Devlin, "Locally-weighted regression: an approach to regression analysis by local fitting," J. Am. Stat. Assoc. 83, 596-610 (1988).
18. H. W. Engel, M. Hanke, and A. Neubauer, Regularization of Ill-Posed Problems (Kluwer, 1996).
19. M. Hanke, "Limitations of the L-curve method in ill-posed problems," BIT 36, 287-301 (1996).
20. A. B. Bakushinskii, "Remarks on choosing a regularization parameter using the quasi-optimality and ratio criterion," USSR Comput. Math. Math. Phys. 24, 181-182 (1985).
21. C. R. Vogel, "Non-convergence of the L-curve regularization parameter selection method," Inverse Probl. 12, 535-547 (1996).
22. T. Regenska, "A regularization parameter in discrete ill-posed problems," SIAM J. Sci. Comput. (USA) 17, 740-749 (1996).
23. D. M. Allen, "The relationship between variable selection and data augmentation and a method for prediction," Technometrics 16, 125-127 (1974).
24. P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, 1986).