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Gaussian Markov random field priors for inverse problems
1. | Department of Mathematical Sciences, University of Montana, Missoula, Montana 59812, United States |
References:
[1] |
J. M. Bardsley, D. Calvetti and E. Somersalo, Hierarchical regularization for edge-preserving reconstruction of PET images, Inverse Problems, 26 (2010), 035010.
doi: 10.1088/0266-5611/26/3/035010. |
[2] |
J. M. Bardsley and J. Goldes, An iterative method for edge-preserving MAP estimation when data-noise is poisson, SIAM J. Sci. Comput., 32 (2010), 171-185.
doi: 10.1137/080726884. |
[3] |
J. M. Bardsley and J. Goldes, Regularization parameter selection methods for ill-posed poisson maximum likelihood estimation, Inverse Problems, 25 (2009), 095005.
doi: 10.1088/0266-5611/25/9/095005. |
[4] |
J. M. Bardsley and C. R. Vogel, A nonnnegatively constrained convex programming method for image reconstruction, SIAM J. Sci. Comput., 25 (2004), 1326-1343.
doi: 10.1137/S1064827502410451. |
[5] |
J. Besag, Spatial interaction and the statistical analysis of lattice systems, J. R. Stat. Soc. Ser. B, 36 (1974), 192-236. |
[6] |
D. Calvetti and E. Somersalo, "Introduction to Bayesian Scientific Computing," Springer, New York, 2007. |
[7] |
D. Calvetti and E. Somersalo, A Gaussian hypermodel to recover blocky objects, Inverse Problems, 23 (2007), 733-754.
doi: 10.1088/0266-5611/23/2/016. |
[8] |
D. Calvetti and E. Somersalo, Hypermodels in the bayesian imaging framework, Inverse Problems, 24 (2008), 034013.
doi: 10.1088/0266-5611/24/3/034013. |
[9] |
D. Calvetti, J. Kaipio and E. Somersalo, Aristotelian prior boundary conditions, Intl. J. Math. Comp. Sci., 1 (2005), 63-81. |
[10] |
H. K. Engl, M. Hanke and A. Neubauer, "Regularization of Inverse Problems," Kluwer, The Netherlands, 1996. |
[11] |
P. C. Hansen, "Discrete Inverse Problems: Insight and Algorithms," SIAM, Philadelphia, 2010.
doi: 10.1137/1.9780898718836. |
[12] |
J. Kaipio, V. Kolehmainen, M. Vauhkonen and E. Somersalo, Inverse problems with structural prior information, Inverse Problems, 15 (1999), 713-729.
doi: 10.1088/0266-5611/15/3/306. |
[13] |
J. Kaipio and E. Somersalo, "Statistical and Computational Inverse Problems," Springer, New York, 2005. |
[14] |
V. Kolehmainen, T. Tarvainen, S. R. Arridge and J. P. Kaipio, Marginalization of uninteresting distributed parameters in inverse problems-application to diffuse optical tomography, Intl. J. Uncertainty Quantification, 1 (2011), 1-17.
doi: 10.1615/Int.J.UncertaintyQuantification.v1.i1.10. |
[15] |
F. Natterer and F. Wübbeling, "Mathematical Methods in Image Reconstruction," SIAM, Philadelphia, 2001.
doi: 10.1137/1.9780898718324. |
[16] |
J. M. Ollinger and J. A. Fessler, Positron-emission tomography, IEEE Signal Processing Magazine, (1997), 43-55.
doi: 10.1109/79.560323. |
[17] |
H. Rue and L. Held, "Gaussian Markov Random Fields: Theory and Applications," Chapman and Hall/CRC, Boca Raton, FL, 2005.
doi: 10.1201/9780203492024. |
[18] |
C. R. Vogel, "Computational Methods for Inverse Problems," SIAM, Philadelphia, 2002.
doi: 10.1137/1.9780898717570. |
[19] |
C. R. Vogel and M. E. Oman, A fast, robust algorithm for total variation based reconstruction of noisy, blurred images, IEEE Trans. Image Process., 7 (1998), 813-824.
doi: 10.1109/83.679423. |
[20] |
D. Watkins, "Fundamentals of Matrix Computations," Wiley, Hoboken, NJ, 2010. |
show all references
References:
[1] |
J. M. Bardsley, D. Calvetti and E. Somersalo, Hierarchical regularization for edge-preserving reconstruction of PET images, Inverse Problems, 26 (2010), 035010.
doi: 10.1088/0266-5611/26/3/035010. |
[2] |
J. M. Bardsley and J. Goldes, An iterative method for edge-preserving MAP estimation when data-noise is poisson, SIAM J. Sci. Comput., 32 (2010), 171-185.
doi: 10.1137/080726884. |
[3] |
J. M. Bardsley and J. Goldes, Regularization parameter selection methods for ill-posed poisson maximum likelihood estimation, Inverse Problems, 25 (2009), 095005.
doi: 10.1088/0266-5611/25/9/095005. |
[4] |
J. M. Bardsley and C. R. Vogel, A nonnnegatively constrained convex programming method for image reconstruction, SIAM J. Sci. Comput., 25 (2004), 1326-1343.
doi: 10.1137/S1064827502410451. |
[5] |
J. Besag, Spatial interaction and the statistical analysis of lattice systems, J. R. Stat. Soc. Ser. B, 36 (1974), 192-236. |
[6] |
D. Calvetti and E. Somersalo, "Introduction to Bayesian Scientific Computing," Springer, New York, 2007. |
[7] |
D. Calvetti and E. Somersalo, A Gaussian hypermodel to recover blocky objects, Inverse Problems, 23 (2007), 733-754.
doi: 10.1088/0266-5611/23/2/016. |
[8] |
D. Calvetti and E. Somersalo, Hypermodels in the bayesian imaging framework, Inverse Problems, 24 (2008), 034013.
doi: 10.1088/0266-5611/24/3/034013. |
[9] |
D. Calvetti, J. Kaipio and E. Somersalo, Aristotelian prior boundary conditions, Intl. J. Math. Comp. Sci., 1 (2005), 63-81. |
[10] |
H. K. Engl, M. Hanke and A. Neubauer, "Regularization of Inverse Problems," Kluwer, The Netherlands, 1996. |
[11] |
P. C. Hansen, "Discrete Inverse Problems: Insight and Algorithms," SIAM, Philadelphia, 2010.
doi: 10.1137/1.9780898718836. |
[12] |
J. Kaipio, V. Kolehmainen, M. Vauhkonen and E. Somersalo, Inverse problems with structural prior information, Inverse Problems, 15 (1999), 713-729.
doi: 10.1088/0266-5611/15/3/306. |
[13] |
J. Kaipio and E. Somersalo, "Statistical and Computational Inverse Problems," Springer, New York, 2005. |
[14] |
V. Kolehmainen, T. Tarvainen, S. R. Arridge and J. P. Kaipio, Marginalization of uninteresting distributed parameters in inverse problems-application to diffuse optical tomography, Intl. J. Uncertainty Quantification, 1 (2011), 1-17.
doi: 10.1615/Int.J.UncertaintyQuantification.v1.i1.10. |
[15] |
F. Natterer and F. Wübbeling, "Mathematical Methods in Image Reconstruction," SIAM, Philadelphia, 2001.
doi: 10.1137/1.9780898718324. |
[16] |
J. M. Ollinger and J. A. Fessler, Positron-emission tomography, IEEE Signal Processing Magazine, (1997), 43-55.
doi: 10.1109/79.560323. |
[17] |
H. Rue and L. Held, "Gaussian Markov Random Fields: Theory and Applications," Chapman and Hall/CRC, Boca Raton, FL, 2005.
doi: 10.1201/9780203492024. |
[18] |
C. R. Vogel, "Computational Methods for Inverse Problems," SIAM, Philadelphia, 2002.
doi: 10.1137/1.9780898717570. |
[19] |
C. R. Vogel and M. E. Oman, A fast, robust algorithm for total variation based reconstruction of noisy, blurred images, IEEE Trans. Image Process., 7 (1998), 813-824.
doi: 10.1109/83.679423. |
[20] |
D. Watkins, "Fundamentals of Matrix Computations," Wiley, Hoboken, NJ, 2010. |
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