Expectation maximization and total variation-based model for computed tomography reconstruction from undersampled data

Progress in Biomedical Optics and Imaging - Proceedings of SPIE

Volumn 7961, Issue , 2011, Pages

  Yan, Ming ^a   Vese, Luminita A ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

compressive sensing; computerized tomography; energy minimization; expectation maximization; image reconstruction; Poisson noise; Radon transform; total variation

Indexed keywords

COMPRESSIVE SENSING; ENERGY MINIMIZATION; EXPECTATION MAXIMIZATION; POISSON NOISE; RADON TRANSFORM; TOTAL VARIATION;

CHANNEL ESTIMATION; IMAGE RECONSTRUCTION; MAXIMUM PRINCIPLE; MEDICAL IMAGING; NUMERICAL METHODS; TOMOGRAPHY;

COMPUTERIZED TOMOGRAPHY;

EID: 79955782137     PISSN: 16057422     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.878238     Document Type: Conference Paper

References (20)

1. C. Brune, A. Sawatzky and M. Burger, Bregman-EM-TV Methods with Application to Optical Nanoscopy, LNCS, vol. 5567, pp. 235-246 (2009).
2. C. Brune, A. Sawatzky and M. Burger, Primal and Dual Bregman Methods with Application to Optical Nanoscopy, UCLA C.A.M. Report 09-47 (2009).
3. A. Dempster, N. Laird and D. Rubin,Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society Series B, vol. 39, pp. 1-38 (1977).
4. Z.T. Harmany, R.F. Marcia, and R.M. Willett, Sparse Poisson intensity reconstruction algorithms, Proceedings of IEEE/SP 15th Workshop on Statistical Signal Processing, pp. 634-637 (2009).
5. S. Jafarpour, R. Willett, M. Raginsky and R. Calderbank, Performance bounds for expander-based compressed sensing in the presence of Poisson noise, Proceedings of the IEEE Forty-Third Asilomar Conference on Signals, Systems and Computers, pp. 513-517 (2009).
6. 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, Med Phys, vol. 37(4), pp. 1757-1760 (2010).
7. M. Jung, E. Resmerita and L.A. Vese, Dual norm based iterative methods for image restoration, UCLA C.A.M. Report 09-88 (2009).
8. A. Kak and M. Slaney, Principles of Computerized Tomographic Imaging, Society of Industrial and Applied Mathematics (2001).
9. W. Karush, Minima of functions of several variables with inequalities as side constraints, M.Sc. Dissertation Department of Mathematics, University of Chicago, Chicago, Illinois (1939).
10. H. Kuhn and A. Tucker, Nonlinear programming, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, pp. 481-492 (1951).
11. T. Le, R. Chartrand and T. Asaki, A Variational Approach to Constructing Images Corrupted by Poisson Noise, JMIV, vol. 27(3), pp. 257-263 (2007). (Pubitemid 46664094)
12. L. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D, vol. 60, pp. 259-268 (1992).
13. L. Rudin and S. Osher, Total variation based image restoration with free local constraints, Proceedings of IEEE International Conference on Image Processing (ICIP), vol. I, pp. 31-35 (1994).
14. S. Setzer, G. Steidl and T. Teuber, Deblurring Poissonian images by split Bregman techniques, J. Visual Communication and Image Representation, vol. 21, pp. 193-199 (2010).
15. L. Shepp and B. Logan, The Fourier Reconstruction of a Head Section, IEEE Transactions on Nuclear Science, vol. 21, pp. 21-34 (1974).
16. L. Shepp and Y. Vardi, Maximum likelihood reconstruction for emission tomography, IEEE Transactions on Medical Imaging, vol. 1, pp. 113-122 (1982). (Pubitemid 13557763)
17. R. Siddon, Fast calculation of the exact radiological path for a three-dimensional CT array, Medical Physics, vol. 12, pp. 252-255 (1986). (Pubitemid 15089015)
18. 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 (ICIP), pp. 4177-4180 (2010).
19. H. Zhao and A.J. Reader, Fast ray-tracing technique to calculate line integral paths in voxel arrays, IEEE Nuclear Science Symposium Conference Record, M11-197 (2003).
20. Compressive Sensing Resources, http://dsp.rice.edu/cs