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General convergent expectation maximization (EM)-type algorithms for image reconstruction
1. | Department of Mathematics, University of California, Los Angeles, Los Angeles, CA 90095, United States |
2. | Department of Radiological Sciences, University of California, Los Angeles, Los Angeles, CA 90095, United States |
3. | Department of Computer Sciences, University of California, Los Angeles, Los Angeles, CA 90095, United States |
4. | Department of Mathematics, University of California, Los Angeles, Los Angeles, CA 90095-1555, United States |
References:
[1] |
R. Acar and C. R. Vogel, Analysis of bounded variation penalty methods for ill-posed problems, Inverse Problems, 10 (1994), 1217-1229.
doi: 10.1088/0266-5611/10/6/003. |
[2] |
R. Alicandro, A. braides and J. Shah, Free-discontinuity problems via functionals involving the $L^1$-norm of the gradient and their approximation, Interfaces and Free Boundaries, 1 (1999), 17-37.
doi: 10.4171/IFB/2. |
[3] |
A. Andersen, Algebraic reconstruction in CT from limited views, IEEE Transactions on Medical Imaging, 8 (1989), 50-55.
doi: 10.1109/42.20361. |
[4] |
A. Andersen and A. Kak, Simultaneous algebraic reconstruction technique (SART): A superior implementation of the ART algorithm, Ultrasonic Imaging, 6 (1984), 81-94.
doi: 10.1177/016173468400600107. |
[5] |
C. Atkinson and J. Soria, An efficient simultaneous reconstruction technique for tomographic particle image velocimetry, Experiments in Fluids, 47 (2009), 553-568.
doi: 10.1007/s00348-009-0728-0. |
[6] |
C. Brune, M. Burger, A. Sawatzky, T. Kosters and F. Wubbeling, Forward-Backward EM-tV methods for inverse problems with poisson noise, Preprint, august 2009. |
[7] |
C. Brune, A. Sawatzky and M. Burger, Bregman-EM-TV methods with application to optical nanoscopy, Lecture Notes in Computer Science, 5567 (2009), 235-246.
doi: 10.1007/978-3-642-02256-2_20. |
[8] |
C. Brune, A. Sawatzky and M. Burger, Primal and dual Bregman methods with application to optical nanoscopy, International Journal of Computer Vision, 92 (2011), 211-229.
doi: 10.1007/s11263-010-0339-5. |
[9] |
Y. Censor and T. Elfving, Block-iterative algorithms with diagonally scaled oblique projections for the linear feasibility problem, SIAM Journal on Matrix Analysis and Applications, 24 (2002), 40-58.
doi: 10.1137/S089547980138705X. |
[10] |
Y. Censor, D. Gordon and R. Gordon, Component averaging: An efficient iterative parallel algorithm for large and sparse unstructured problems, Parallel Computing, 27 (2001), 777-808.
doi: 10.1016/S0167-8191(00)00100-9. |
[11] |
J. Chen, J. Cong, L. A. Vese, J. D. Villasenor, M. Yan and Y. Zou, A hybrid architecture for compressive sensing 3-D CT reconstruction, IEEE Journal on Emerging and Selected Topics in Circuits and Systems, 2 (2012), 616-625.
doi: 10.1109/JETCAS.2012.2221530. |
[12] |
J. A. Conchello and J. G. McNally, Fast regularization technique for expectation maximization algorithm for optical sectioning microscopy, in "Proceeding of SPIE Symposium on Electronic Imaging Science and Technology," 2655 (1996), 199-208.
doi: 10.1117/12.237477. |
[13] |
A. Dempster, N. Laird and D. Rubin, Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society Series B, 39 (1977), 1-38. |
[14] |
N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo-Marin and J. Zerubia, Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution, Microscopy Research and Technique, 69 (2006), 260-266.
doi: 10.1002/jemt.20294. |
[15] |
S. Geman and D. Geman, Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, IEEE Transactions on Pattern Analysis and Machine Intelligence, 6 (1984), 721-741.
doi: 10.1109/TPAMI.1984.4767596. |
[16] |
R. Gordon, R. Bender and G. Herman, Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography, Journal of Theoretical Biology, 29 (1970), 471-481.
doi: 10.1016/0022-5193(70)90109-8. |
[17] |
P. J. Green, On use of the EM algorithm for penalized likelihood estimation, Journal of the Royal Statistical Society Series B, 52 (1990), 443-452.
doi: 10.2307/2345668. |
[18] |
U. Grenander, "Tutorial in Pattern Theory," Lecture Notes Volume, Division of Applied Mathematics, Brown University, 1984. |
[19] |
Z. T. Harmany, R. F. Marcia and R. M. Willett, Sparse Poisson intensity reconstruction algorithms, in "Proceedings of IEEE/SP 15th Workshop on Statistical Signal Processing,'' (2009), 634-637.
doi: 10.1109/SSP.2009.5278495. |
[20] |
G. Herman, "Fundamentals of Computerized Tomography: Image Reconstruction From Projection," Second edition. Advances in Pattern Recognition. Springer, Dordrecht, 2009.
doi: 10.1007/978-1-84628-723-7. |
[21] |
H. Hurwitz, Entropy reduction in Bayesian analysis of measurements, Physics Review A, 12 (1975), 698-706.
doi: 10.1103/PhysRevA.12.698. |
[22] |
S. Jafarpour, R. Willett, M. Raginsky and R. Calderbank, Performance bounds for expander-based compressed sensing in the presence of Poisson noise, in "Proceedings of the IEEE Forty-Third Asilomar Conference on Signals, Systems and Computers," (2009), 513-517.
doi: 10.1109/ACSSC.2009.5469879. |
[23] |
X. Jia, Y. Lou, R. Li, W. Y. Song and S. B. Jiang, GPU-based fast cone beam CT reconstruction from undersampled and noisy projection data via total variation, Medical Physics, 37 (2010), 1757-1760.
doi: 10.1118/1.3371691. |
[24] |
M. Jiang and G. Wang, Convergence of the simultaneous algebraic reconstruction technique (SART), IEEE Transaction on Image Processing, 12 (2003), 957-961.
doi: 10.1109/TIP.2003.815295. |
[25] |
M. Jiang and G. Wang, Convergence studies on iterative algorithms for image reconstruction, IEEE Transactions on Medical Imaging, 22 (2003), 569-579.
doi: 10.1109/TMI.2003.812253. |
[26] |
S. Joshi and M. I. Miller, Maximum a posteriori estimation with Good's roughness for three-dimensional optical sectioning microscopy, Journal of the Optical Society of America A, 10 (1993), 1078-1085.
doi: 10.1364/JOSAA.10.001078. |
[27] |
M. Jung, E. Resmerita and L. A. Vese, Dual norm based iterative methods for image restoration, Journal of Mathematical Imaging and Vision, 44 (2012), 128-149.
doi: 10.1007/s10851-011-0318-7. |
[28] |
A. Kak and M. Slaney, "Principles of Computerized Tomographic Imaging," Reprint of the 1988 original. Classics in Applied Mathematics, 33. Society of Industrial and Applied Mathematics(SIAM), Philadelphia, PA, 2001.
doi: 10.1137/1.9780898719277. |
[29] |
W. Karush, "Minima of Functions of Several Variables With Inequalities as Side Constraints,'' Master's thesis, Department of Mathematics, University of Chicago, Chicago, Illinois, 1939. |
[30] |
H. Kuhn and A. Tucker, Nonlinear programming, in "Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability," 1950, pp. 481–492. University of California Press, Berkeley and Los Angeles, 1951. |
[31] |
T. Le, R. Chartrand and T. J. Asaki, A variational approach to reconstructing images corrupted by Poisson noise, Journal of Mathematical Imaging and Vision, 27 (2007), 257-263.
doi: 10.1007/s10851-007-0652-y. |
[32] |
E. Levitan and G. T. Herman, A maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission tomography, IEEE Transactions on Medial Imaging, 6 (1987), 185-192.
doi: 10.1109/TMI.1987.4307826. |
[33] |
L. B. Lucy, An iterative technique for the rectification of observed distributions, Astronomical Journal, 79 (1974), 745-754.
doi: 10.1086/111605. |
[34] |
J. Markham and J. A. Conchello, Fast maximum-likelihood image-restoration algorithms for three-dimensional fluorescence microscopy, Journal of the Optical Society America A, 18 (2001), 1062-1071.
doi: 10.1364/JOSAA.18.001062. |
[35] |
F. Natterer and F. Wubbeling, "Mathematical Methods in Image Reconstruction," SIAM Monographs on Mathematical Modeling and Computation. Society for Industrial and Applied Mathematics, Philadelphia, PA, 2001.
doi: 10.1137/1.9780898718324. |
[36] |
Y. Pan, R. Whitaker, A. Cheryauka and D. Ferguson, Feasibility of GPU-assisted iterative image reconstruction for mobile C-arm CT, in "Proceedings of International Society for Photonics and Optonics,'' SPIE, 7258 (2009), 72585J.
doi: 10.1117/12.812162. |
[37] |
W. H. Richardson, Bayesian-based iterative method of image restoration, Journal of the Optical Society America, 62 (1972), 55-59.
doi: 10.1364/JOSA.62.000055. |
[38] |
L. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D, 60 (1992), 259-268.
doi: 10.1016/0167-2789(92)90242-F. |
[39] |
S. Setzer, G. Steidl and T. Teuber, Deblurring Poissonian images by split Bregman techniques, Journal of Visual Communication and Image Representation, 21 (2010), 193-199.
doi: 10.1016/j.jvcir.2009.10.006. |
[40] |
H. Shah, A common framework for curve evolution, segmentation and anisotropic diffusion, in "Proceeding of IEEE Conference on Computer Vision and Pattern Recognition," (1996), 136-142.
doi: 10.1109/CVPR.1996.517065. |
[41] |
L. Shepp and B. Logan, The Fourier reconstruction of a head section, IEEE Transaction on Nuclear Science, 21 (1974), 21-34.
doi: 10.1109/TNS.1974.6499235. |
[42] |
L. Shepp and Y. Vardi, Maximum likelihood reconstruction for emission tomography, IEEE Transaction on Medical Imaging, 1 (1982), 113-122.
doi: 10.1109/tmi.1982.4307558. |
[43] |
R. Siddon, Fast calculation of the exact radiological path for a three-dimensional CT array, Medical Physics, 12 (1985), 252-255.
doi: 10.1118/1.595715. |
[44] |
E. Y. Sidky, R. Chartrand and X. Pan, Image reconstruction from few views by non-convex optimization, in "IEEE Nuclear Science Symposium Conference Record,'' 5 (2007), 3526-3530. .
doi: 10.1109/NSSMIC.2007.4436889. |
[45] |
E. Y Sidky, J. H. Jorgensen and X. Pan, Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm, Physics in Medicine and Biology, 57 (2012), 3065.
doi: 10.1088/0031-9155/57/10/3065. |
[46] |
A. N. Tychonoff and V. Y. Arsenin, "Solution of Ill-posed Problems," Winston & Sons, Washington, 1977. |
[47] |
J. Wang and Y. Zheng, On the convergence of generalized simultaneous iterative reconstruction algorithms, IEEE Transaction on Image Processing, 16 (2007), 1-6.
doi: 10.1109/TIP.2006.887725. |
[48] |
R. M. Willett, Z. T. Harmany and R. F. Marcia, Poisson image reconstruction with total variation regularization, Proceedings of 17th IEEE International Conference on Image Processing, (2010), 4177-4180.
doi: 10.1109/ICIP.2010.5649600. |
[49] |
M. Yan and L. A. Vese, Expectation maximization and total variation based model for computed tomography reconstruction from undersampled data, in "Proceeding of SPIE Medical Imaging: Physics of Medical Imaging," 7961 (2011), 79612X.
doi: 10.1117/12.878238. |
[50] |
M. Yan, Convergence analysis of SART: Optimization and statistics, International Journal of Computer Mathematics, 90 (2013), 30-47.
doi: 10.1080/00207160.2012.709933. |
[51] |
M. Yan, J. Chen, L. A. Vese, J. D. Villasenor, A. A. T. Bui and J. Cong, EM+TV based reconstruction for cone-beam CT with reduced radiation, in "Lecture Notes in Computer Science," 6938 (2011), 1-10.
doi: 10.1007/978-3-642-24028-7_1. |
[52] |
H. Yu and G. Wang, SART-type image reconstruction from a limited number of projections with the sparsity constraint, Journal of Biomedical Imaging, 2010 (2010), 1-9.
doi: 10.1155/2010/934847. |
[53] |
H. Zhao and A. J. Reader, Fast ray-tracing technique to calculate line integral paths in voxel arrays, in IEEE Nuclear Science Symposium Conference Record, 4 (2003), 2808-2812.
doi: 10.1109/NSSMIC.2003.1352469. |
[54] |
D. Zhu, M. Razaz and R. Lee, Adaptive penalty likelihood for reconstruction of multi-dimensional confocal microscopy images, Computerized Medical Imaging and Graphics, 29 (2005), 319-331.
doi: 10.1016/j.compmedimag.2004.12.004. |
[55] |
, Compressive Sensing Resources,, , ().
|
show all references
References:
[1] |
R. Acar and C. R. Vogel, Analysis of bounded variation penalty methods for ill-posed problems, Inverse Problems, 10 (1994), 1217-1229.
doi: 10.1088/0266-5611/10/6/003. |
[2] |
R. Alicandro, A. braides and J. Shah, Free-discontinuity problems via functionals involving the $L^1$-norm of the gradient and their approximation, Interfaces and Free Boundaries, 1 (1999), 17-37.
doi: 10.4171/IFB/2. |
[3] |
A. Andersen, Algebraic reconstruction in CT from limited views, IEEE Transactions on Medical Imaging, 8 (1989), 50-55.
doi: 10.1109/42.20361. |
[4] |
A. Andersen and A. Kak, Simultaneous algebraic reconstruction technique (SART): A superior implementation of the ART algorithm, Ultrasonic Imaging, 6 (1984), 81-94.
doi: 10.1177/016173468400600107. |
[5] |
C. Atkinson and J. Soria, An efficient simultaneous reconstruction technique for tomographic particle image velocimetry, Experiments in Fluids, 47 (2009), 553-568.
doi: 10.1007/s00348-009-0728-0. |
[6] |
C. Brune, M. Burger, A. Sawatzky, T. Kosters and F. Wubbeling, Forward-Backward EM-tV methods for inverse problems with poisson noise, Preprint, august 2009. |
[7] |
C. Brune, A. Sawatzky and M. Burger, Bregman-EM-TV methods with application to optical nanoscopy, Lecture Notes in Computer Science, 5567 (2009), 235-246.
doi: 10.1007/978-3-642-02256-2_20. |
[8] |
C. Brune, A. Sawatzky and M. Burger, Primal and dual Bregman methods with application to optical nanoscopy, International Journal of Computer Vision, 92 (2011), 211-229.
doi: 10.1007/s11263-010-0339-5. |
[9] |
Y. Censor and T. Elfving, Block-iterative algorithms with diagonally scaled oblique projections for the linear feasibility problem, SIAM Journal on Matrix Analysis and Applications, 24 (2002), 40-58.
doi: 10.1137/S089547980138705X. |
[10] |
Y. Censor, D. Gordon and R. Gordon, Component averaging: An efficient iterative parallel algorithm for large and sparse unstructured problems, Parallel Computing, 27 (2001), 777-808.
doi: 10.1016/S0167-8191(00)00100-9. |
[11] |
J. Chen, J. Cong, L. A. Vese, J. D. Villasenor, M. Yan and Y. Zou, A hybrid architecture for compressive sensing 3-D CT reconstruction, IEEE Journal on Emerging and Selected Topics in Circuits and Systems, 2 (2012), 616-625.
doi: 10.1109/JETCAS.2012.2221530. |
[12] |
J. A. Conchello and J. G. McNally, Fast regularization technique for expectation maximization algorithm for optical sectioning microscopy, in "Proceeding of SPIE Symposium on Electronic Imaging Science and Technology," 2655 (1996), 199-208.
doi: 10.1117/12.237477. |
[13] |
A. Dempster, N. Laird and D. Rubin, Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society Series B, 39 (1977), 1-38. |
[14] |
N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo-Marin and J. Zerubia, Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution, Microscopy Research and Technique, 69 (2006), 260-266.
doi: 10.1002/jemt.20294. |
[15] |
S. Geman and D. Geman, Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, IEEE Transactions on Pattern Analysis and Machine Intelligence, 6 (1984), 721-741.
doi: 10.1109/TPAMI.1984.4767596. |
[16] |
R. Gordon, R. Bender and G. Herman, Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography, Journal of Theoretical Biology, 29 (1970), 471-481.
doi: 10.1016/0022-5193(70)90109-8. |
[17] |
P. J. Green, On use of the EM algorithm for penalized likelihood estimation, Journal of the Royal Statistical Society Series B, 52 (1990), 443-452.
doi: 10.2307/2345668. |
[18] |
U. Grenander, "Tutorial in Pattern Theory," Lecture Notes Volume, Division of Applied Mathematics, Brown University, 1984. |
[19] |
Z. T. Harmany, R. F. Marcia and R. M. Willett, Sparse Poisson intensity reconstruction algorithms, in "Proceedings of IEEE/SP 15th Workshop on Statistical Signal Processing,'' (2009), 634-637.
doi: 10.1109/SSP.2009.5278495. |
[20] |
G. Herman, "Fundamentals of Computerized Tomography: Image Reconstruction From Projection," Second edition. Advances in Pattern Recognition. Springer, Dordrecht, 2009.
doi: 10.1007/978-1-84628-723-7. |
[21] |
H. Hurwitz, Entropy reduction in Bayesian analysis of measurements, Physics Review A, 12 (1975), 698-706.
doi: 10.1103/PhysRevA.12.698. |
[22] |
S. Jafarpour, R. Willett, M. Raginsky and R. Calderbank, Performance bounds for expander-based compressed sensing in the presence of Poisson noise, in "Proceedings of the IEEE Forty-Third Asilomar Conference on Signals, Systems and Computers," (2009), 513-517.
doi: 10.1109/ACSSC.2009.5469879. |
[23] |
X. Jia, Y. Lou, R. Li, W. Y. Song and S. B. Jiang, GPU-based fast cone beam CT reconstruction from undersampled and noisy projection data via total variation, Medical Physics, 37 (2010), 1757-1760.
doi: 10.1118/1.3371691. |
[24] |
M. Jiang and G. Wang, Convergence of the simultaneous algebraic reconstruction technique (SART), IEEE Transaction on Image Processing, 12 (2003), 957-961.
doi: 10.1109/TIP.2003.815295. |
[25] |
M. Jiang and G. Wang, Convergence studies on iterative algorithms for image reconstruction, IEEE Transactions on Medical Imaging, 22 (2003), 569-579.
doi: 10.1109/TMI.2003.812253. |
[26] |
S. Joshi and M. I. Miller, Maximum a posteriori estimation with Good's roughness for three-dimensional optical sectioning microscopy, Journal of the Optical Society of America A, 10 (1993), 1078-1085.
doi: 10.1364/JOSAA.10.001078. |
[27] |
M. Jung, E. Resmerita and L. A. Vese, Dual norm based iterative methods for image restoration, Journal of Mathematical Imaging and Vision, 44 (2012), 128-149.
doi: 10.1007/s10851-011-0318-7. |
[28] |
A. Kak and M. Slaney, "Principles of Computerized Tomographic Imaging," Reprint of the 1988 original. Classics in Applied Mathematics, 33. Society of Industrial and Applied Mathematics(SIAM), Philadelphia, PA, 2001.
doi: 10.1137/1.9780898719277. |
[29] |
W. Karush, "Minima of Functions of Several Variables With Inequalities as Side Constraints,'' Master's thesis, Department of Mathematics, University of Chicago, Chicago, Illinois, 1939. |
[30] |
H. Kuhn and A. Tucker, Nonlinear programming, in "Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability," 1950, pp. 481–492. University of California Press, Berkeley and Los Angeles, 1951. |
[31] |
T. Le, R. Chartrand and T. J. Asaki, A variational approach to reconstructing images corrupted by Poisson noise, Journal of Mathematical Imaging and Vision, 27 (2007), 257-263.
doi: 10.1007/s10851-007-0652-y. |
[32] |
E. Levitan and G. T. Herman, A maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission tomography, IEEE Transactions on Medial Imaging, 6 (1987), 185-192.
doi: 10.1109/TMI.1987.4307826. |
[33] |
L. B. Lucy, An iterative technique for the rectification of observed distributions, Astronomical Journal, 79 (1974), 745-754.
doi: 10.1086/111605. |
[34] |
J. Markham and J. A. Conchello, Fast maximum-likelihood image-restoration algorithms for three-dimensional fluorescence microscopy, Journal of the Optical Society America A, 18 (2001), 1062-1071.
doi: 10.1364/JOSAA.18.001062. |
[35] |
F. Natterer and F. Wubbeling, "Mathematical Methods in Image Reconstruction," SIAM Monographs on Mathematical Modeling and Computation. Society for Industrial and Applied Mathematics, Philadelphia, PA, 2001.
doi: 10.1137/1.9780898718324. |
[36] |
Y. Pan, R. Whitaker, A. Cheryauka and D. Ferguson, Feasibility of GPU-assisted iterative image reconstruction for mobile C-arm CT, in "Proceedings of International Society for Photonics and Optonics,'' SPIE, 7258 (2009), 72585J.
doi: 10.1117/12.812162. |
[37] |
W. H. Richardson, Bayesian-based iterative method of image restoration, Journal of the Optical Society America, 62 (1972), 55-59.
doi: 10.1364/JOSA.62.000055. |
[38] |
L. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D, 60 (1992), 259-268.
doi: 10.1016/0167-2789(92)90242-F. |
[39] |
S. Setzer, G. Steidl and T. Teuber, Deblurring Poissonian images by split Bregman techniques, Journal of Visual Communication and Image Representation, 21 (2010), 193-199.
doi: 10.1016/j.jvcir.2009.10.006. |
[40] |
H. Shah, A common framework for curve evolution, segmentation and anisotropic diffusion, in "Proceeding of IEEE Conference on Computer Vision and Pattern Recognition," (1996), 136-142.
doi: 10.1109/CVPR.1996.517065. |
[41] |
L. Shepp and B. Logan, The Fourier reconstruction of a head section, IEEE Transaction on Nuclear Science, 21 (1974), 21-34.
doi: 10.1109/TNS.1974.6499235. |
[42] |
L. Shepp and Y. Vardi, Maximum likelihood reconstruction for emission tomography, IEEE Transaction on Medical Imaging, 1 (1982), 113-122.
doi: 10.1109/tmi.1982.4307558. |
[43] |
R. Siddon, Fast calculation of the exact radiological path for a three-dimensional CT array, Medical Physics, 12 (1985), 252-255.
doi: 10.1118/1.595715. |
[44] |
E. Y. Sidky, R. Chartrand and X. Pan, Image reconstruction from few views by non-convex optimization, in "IEEE Nuclear Science Symposium Conference Record,'' 5 (2007), 3526-3530. .
doi: 10.1109/NSSMIC.2007.4436889. |
[45] |
E. Y Sidky, J. H. Jorgensen and X. Pan, Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm, Physics in Medicine and Biology, 57 (2012), 3065.
doi: 10.1088/0031-9155/57/10/3065. |
[46] |
A. N. Tychonoff and V. Y. Arsenin, "Solution of Ill-posed Problems," Winston & Sons, Washington, 1977. |
[47] |
J. Wang and Y. Zheng, On the convergence of generalized simultaneous iterative reconstruction algorithms, IEEE Transaction on Image Processing, 16 (2007), 1-6.
doi: 10.1109/TIP.2006.887725. |
[48] |
R. M. Willett, Z. T. Harmany and R. F. Marcia, Poisson image reconstruction with total variation regularization, Proceedings of 17th IEEE International Conference on Image Processing, (2010), 4177-4180.
doi: 10.1109/ICIP.2010.5649600. |
[49] |
M. Yan and L. A. Vese, Expectation maximization and total variation based model for computed tomography reconstruction from undersampled data, in "Proceeding of SPIE Medical Imaging: Physics of Medical Imaging," 7961 (2011), 79612X.
doi: 10.1117/12.878238. |
[50] |
M. Yan, Convergence analysis of SART: Optimization and statistics, International Journal of Computer Mathematics, 90 (2013), 30-47.
doi: 10.1080/00207160.2012.709933. |
[51] |
M. Yan, J. Chen, L. A. Vese, J. D. Villasenor, A. A. T. Bui and J. Cong, EM+TV based reconstruction for cone-beam CT with reduced radiation, in "Lecture Notes in Computer Science," 6938 (2011), 1-10.
doi: 10.1007/978-3-642-24028-7_1. |
[52] |
H. Yu and G. Wang, SART-type image reconstruction from a limited number of projections with the sparsity constraint, Journal of Biomedical Imaging, 2010 (2010), 1-9.
doi: 10.1155/2010/934847. |
[53] |
H. Zhao and A. J. Reader, Fast ray-tracing technique to calculate line integral paths in voxel arrays, in IEEE Nuclear Science Symposium Conference Record, 4 (2003), 2808-2812.
doi: 10.1109/NSSMIC.2003.1352469. |
[54] |
D. Zhu, M. Razaz and R. Lee, Adaptive penalty likelihood for reconstruction of multi-dimensional confocal microscopy images, Computerized Medical Imaging and Graphics, 29 (2005), 319-331.
doi: 10.1016/j.compmedimag.2004.12.004. |
[55] |
, Compressive Sensing Resources,, , ().
|
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