A theoretical framework for the regularization of poisson likelihood estimation problems

Inverse Problems and Imaging

Volumn 4, Issue 1, 2010, Pages 11-17

  Bardsley, Johnathan M ^a  

^a UNIVERSITY OF MONTANA   (United States)

Author keywords

Mathematical imaging; Poisson likelihood; Regularization; Variational problems

Indexed keywords

EID: 77349108828     PISSN: 19308337     EISSN: 19308345     Source Type: Journal    
DOI: 10.3934/ipi.2010.4.11     Document Type: Article

References (12)

1. R. Acar and C. R. Vogel, Analysis of bounded variation penalty methods for ill-posed problems, Inverse Problems, 10 (1994), 1217-1229.
2. J. M. Bardsley and N'djekornom Laobeul, Tikhonov regularized poisson likelihood estimation: Theoritical justification and a computational method, Inverse Problems in Science and Engineering, 16 (2008), 199-215.
3. J. M. Bardsley and N'djekornom Laobeul, An analysis of regularization by diffusion for illposed poisson likelihood estimation, Inverse Problems in Science and Engineering, 17 (2009), 537-550.
4. J. M. Bardsley and A. Luttman, Total variation-penalized poisson likelihood estimation for ill-posed problems, Advances in Computational Mathematics, 31 (2009), 35-59.
5. Lawrence C. Evans, Partial Differential Equations," American Mathematical Society, Providence, Rhode Island, 2002.
6. Lawrence C. Evans and Ronald Gariepy, "Measure Theory and Fine Properties of Functions," CRC Press, Boca Raton, 1992.
7. T. Le, R. Chartrand and T. J. Asaki, A variational approach to reconstructing images corruted by poisson noise, Journal of Mathematical Imaging and Vision, 27 (2007), 257-263.
8. John M. Ollinger and Jeffrey A. Fessler, Positron emission tomography, IEEE Signal Processing Magazine, 14 (1997), 43-55.
9. D. L. Snyder, A. M. Hammoud and R. L. White, Image recovery from data acquired with a charge-coupled-device camera, Journal of the Optical Society of America A, 10 (1993), 1014-1023.
10. A. N. Tikhonov, A.V. Goncharsky, V. V. Stepanov and A. G. Yagola, "Numerical Methods for the Solution of Ill-Posed Problems," Kluwer Academic Publishers, 1990.
11. C. R. Vogel, Computational Methods for Inverse Problems, SIAM, Philadelphia, 2002.
12. Eberhard Zeidler, "Applied Functional Analysis: Applications to Mathematical Physics, Springer, New York, 1995.