Development and optimization of regularized tomographic reconstruction algorithms utilizing equally-sloped tomography

IEEE Transactions on Image Processing

Volumn 19, Issue 5, 2010, Pages 1259-1268

  Mao, Yu ^a   Fahimian, Benjamin P ^b   Osher, Stanley J ^a   Miao, Jianwei ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Bregman regularization; Continuative regularization; Equally sloped tomography; Operator splitting method; Pseudo polar Fourier transform

Indexed keywords

BROAD APPLICATION; COHERENT DIFFRACTION; COMPUTATIONAL TIME; COMPUTED TOMOGRAPHY; CONSTRAINED PROBLEM; CONTINUATIVE REGULARIZATION; EQUALLY-SLOPED TOMOGRAPHY; ITERATIVE ALGORITHM; LINEAR PROBLEMS; MATHEMATICAL FORMULATION; NUMERICAL EXPERIMENTS; OPERATOR SPLITTING METHOD; PHYSICAL CONSTRAINTS; RADIATION DOSE REDUCTIONS; REGULARIZATION SCHEMES; TOMOGRAPHIC; TOMOGRAPHIC IMAGE RECONSTRUCTION; TOMOGRAPHIC RECONSTRUCTION; TOTAL VARIATION; X-RAY TOMOGRAPHY;

ALGORITHMS; COMPUTERIZED TOMOGRAPHY; FOURIER TRANSFORMS; IMAGE QUALITY; IMAGE RECONSTRUCTION; MATHEMATICAL OPERATORS; MATHEMATICAL TRANSFORMATIONS; NUCLEAR INSTRUMENTATION; OPTIMIZATION; REPAIR; SCANNING ELECTRON MICROSCOPY;

ITERATIVE METHODS;

ALGORITHM; ARTICLE; COMPUTER ASSISTED DIAGNOSIS; COMPUTER GRAPHICS; IMAGE ENHANCEMENT; MATHEMATICAL COMPUTING; METHODOLOGY; OPTICAL TOMOGRAPHY; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING;

ALGORITHMS; COMPUTER GRAPHICS; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING, COMPUTER-ASSISTED; TOMOGRAPHY, OPTICAL;

EID: 77951272520     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2009.2039660     Document Type: Article

References (45)

1. J. Miao, F. Förster, and O. Levi, "Equally sloped tomography with oversampling reconstruction," Phys. Rev. B, vol.72, no.5, p. 52103, 2005. (Pubitemid 43406317)
2. J. Miao, C. Chen, C. Song, Y. Nishino, Y. Kohmura, T. Ishikawa, D. Ramunno-Johnson, T. Lee, and S. Risbud, "Three-dimensional GaNGa2O3 core shell structure revealed by x-ray diffraction microscopy," Phys. Rev. Lett., vol.97, no.21, p. 215503, 2006. (Pubitemid 44791122)
3. J. Miao, T. Ishikawa, Q. Shen, and T. Earnest, "Extending X-ray crystallography to allow the imaging of noncrystalline materials, cells, and single protein complexes," Annu. Rev. Phys. Chem., vol.59, p. 387, 2008. (Pubitemid 351703392)
4. C. Chen, J. Miao, and T. Lee, "Tomographic image alignment in threedimensional coherent diffraction microscopy," Phys. Rev. B, vol.79, p. 052102, 2009.
5. E. Lee, B. Fahimian, C. Iancu, C. Suloway, G. Murphy, E. Wright, D. Castaño-Díez, G. Jensen, and J. Miao, "Radiation dose reduction and image enhancement in biological imaging through equally-sloped tomography," J. Struct. Biol., vol.164, no.2, pp. 221-227, 2008.
6. B. Fahimian, A. Chatziioannou, Y. Mao, and J. Miao, Equally-Sloped Tomography and Its Applications to Radiation Dose Reduction in Transmission CT.
7. A. Kak and M. Slaney, Principles of Computerized Tomographic Imaging. New York: IEEE, 1988, I. E. in Medicine, and B. Society.
8. J. Frank, Electron Tomography: Methods for Three-Dimensional Visualization of Structures in the Cell. New York: Springer, 2006.
9. F. Natterer, The Mathematics of Computerized Tomography. Philadelphia, PA: SIAM, 2001.
10. A. Averbuch, R. Coifman, D. Donoho, M. Israeli, and Y. Shkolnisky, "A framework for discrete integral transformations I-The pseudopolar fourier transform," SIAM J. Sci. Comput., vol.30, pp. 785-803, 2008.
11. A. Averbuch, R. Coifman, D. Donoho, M. Elad, and M. Israeli, "Fast and accurate polar Fourier transform," Appl. Comput. Harmon. Anal., vol.21, no.2, pp. 145-167, 2006. (Pubitemid 44311044)
12. J. Miao, D. Sayre, and H. Chapman, "Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects," J. Opt. Soc. Amer. A, vol.15, no.6, pp. 1662-1669, 1998. (Pubitemid 128572161)
13. J. Miao, P. Charalambous, J. Kirz, and D. Sayre, "Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens," Nature, vol.400, no.6742, pp. 342-344, 1999. (Pubitemid 29344194)
14. D. Sayre, "Some implications of a theorem due to Shannon," Acta Cryst., vol.5, no.6, p. 843, 1952.
15. R. Mersereau and A. Oppenheim, "Digital reconstruction of multidimensional signals from their projections," Proc. IEEE, vol.62, no.10, pp. 1319-1338, Oct. 1974.
16. A. Averbuch, R. Coifman, D. Donoho, M. Israeli, Y. Shkolnisky, and I. Sedelnikov, "A framework for discrete integral transformations II-The 2D discrete Radon transform," SIAM J. Sci. Comput., vol.30, no.2, pp. 785-803, 2008.
17. L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Phys. D, vol.60, no.1-4, pp. 259-268, 1992.
18. A. Buades, B. Coll, and J. Morel, "A review of image denoising algorithms, with a new one," Multiscale Model. Simul., vol.4, no.2, p. 490, 2005. (Pubitemid 43890582)
19. S. Osher,M. Burger, D. Goldfarb, J. Xu, and W. Yin, "An iterative regularization method for total variation based image restoration," Multiscale Model. Simul., vol.4, no.2, pp. 460-489, 2005. (Pubitemid 43885248)
20. E. Candes, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inf. Theory, vol.52, no.2, pp. 489-509, 2006. (Pubitemid 43174093)
21. 1 -minimization with applications to compressed sensing," SIAM J. Imag. Sci., vol.1, no.1, pp. 143-168, 2008.
22. S. Osher, Y.Mao, B. Dong, and W. Yin, "Fast linearized bregman iteration for compressive sensing and sparse denoising," Commun. Math. Sci., 2009.
23. Y. Wang, J. Yang, W. Yin, and Y. Zhang, "A new alternating minimization algorithm for total variation image reconstruction," SIAM J. Imag. Sci., vol.1, pp. 248-272, 2008.
24. L. He, A. Marquina, and S. Osher, "Blind deconvolution using TV regularization and Bregman iteration," Int. J. Imag. Syst. Technol., vol.15, no.1, p. 74, 2005. (Pubitemid 41364767)
25. J. Xu and S. Osher, "Iterative regularization and nonlinear inverse scale space applied to wavelet-based denoising," IEEE Trans. Image Process., vol.16, no.2, p. 534, Feb. 2007. (Pubitemid 46421693)
26. L. He, T.-C. Chang, and S. Osher, "MR image reconstruction from sparse radial samples by using iterative refinement procedures," in Proc. 13th Annu. Meet. ISMRM, 2006, p. 696.
27. J. Cai, E. Candes, and Z. Shen, A Singular Value Thresholding Algorithm for Matrix Completion Oct. 2008 [Online]. Available: http://arxiv.org/pdf/0810. 3286 [Online]. Available: http://arxiv.org/abs/0810.3286
28. P. Lions and B. Mercier, "Splitting algorithms for the sum of two nonlinear operators," SIAM J. Numer. Anal., vol.16, p. 964, 1979.
29. G. Passty, "Ergodic convergence to a zero of the sum of monotone operators in Hilbert space," J. Math. Anal. Appl., vol.72, no.2, pp. 383-390, 1979.
30. P. Combettes and V. Wajs, "Signal recovery by proximal forwardbackward splitting," Multiscale Model. Simul., vol.4, no.4, p. 1168, 2006. (Pubitemid 44932287)
31. M. Figueiredo and R. Nowak,"Wavelet-based adaptive image deconvolution," presented at the IEEE Int. Conf. Acoustics, Speech, and Signal Processing, 2002. (Pubitemid 34710632)
32. A. Chambolle, R. DeVore, N. Lee, and B. Lucier, "Nonlinear wavelet image processing: Variational problems, compression, and noise removal through wavelet shrinkage," IEEE Trans. Image Process., vol.7, no.3, p. 319, Mar. 1998. (Pubitemid 128745350)
33. I. Daubechies, M. Defrise, and C. De Mol, "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint," Commun. Pure Appl. Math., vol.57, no.11, pp. 1413-1457, 2004. (Pubitemid 39427442)
34. M. Elad, B. Matalon, and M. Zibulevsky, "Coordinate and subspace optimization methods for linear least squares with non-quadratic regularization," Appl. Comput. Harmon. Anal., vol.23, no.3, pp. 346-367, 2007. (Pubitemid 47552874)
35. E. Hale, W. Yin, and Y. Zhang, "Fixed-point continuation for -minimization: Methodology and convergence," SIAM J. Optim., vol.19, p. 1107, 2008.
36. Y. Wang, W. Yin, and Y. Zhang, Experimental Report of Fixed Point-Continuation for TotalVariation Minimization.
37. X. Zhang, M. Burger,X. Bresson, and S. Osher, Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction [Online]. Available: ftp://ftp.math.ucla.edu/pub/camreport/cam09-03.pdf
38. J. Darbon and S. Osher, Fast Discrete Optimizations for Sparse Approximations and Deconvolutions preprint, 2007.
39. D. Goldfarb and W. Yin, Parametric Maximum Flow Algorithms for Fast Total Variation Minimization [Online]. Available: http://www.caam.rice.edu/wy1/ paperfiles/
40. J. Darbon and M. Sigelle, "A fast and exact algorithm for total variation minimization," in Proc. 2nd Iberian Conf. Pattern Recognition and Image Analysis, 2005, vol.3522, pp. 351-359, Springer. (Pubitemid 41351469)
41. L. Bregman, "The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming," USSR Computational Mathematics and Mathematical Physics, vol.7, no.3, pp. 200-217, 1967.
42. I. Ekeland and R. Temam, Convex Analysis and Variational Problems. Philadelphia, PA: SIAM, 1999.
43. J. Nocedal and S. Wright, Numerical Optimization. New York: Springer, 1999.
44. I. Zubal, C. Harrell, E. Smith, Z. Rattner, G. Gindi, and P. Hoffer, "Computerized three-dimensional segmented human anatomy," Med. Phys., vol.21, p. 299, 1994. (Pubitemid 24068796)
45. K. Moreland and E. Angel, "The FFT on a GPU," in Proc. ACM SIGGRAPH/EUROGRAPHICS Conf. Graphics Hardware, Switzerland, 2003, pp. 112-119, Eurographics Association Aire-la-Ville, Switzerland.