Dynamic PET reconstruction using wavelet regularization with adapted basis functions

IEEE Transactions on Medical Imaging

Volumn 27, Issue 7, 2008, Pages 943-959

  Verhaeghe, Jeroen ^b   Van De Ville, Dimitri ^a,c   Khalidov, Ildar ^c   D'Asseler, Yves ^a,d   Lemahieu, Ignace ^a,b   Unser, Michael ^a,c  

^a IEEE

^b GHENT UNIVERSITY   (Belgium)

^c EPFL   (Switzerland)

^d GHENT UNIVERSITY HOSPITAL   (Belgium)

Author keywords

Differential system; E spline wavelets; l1 regularization; Spatio temporal positron emission tomography (PET) reconstruction; Time activity curves

Indexed keywords

ACOUSTIC EMISSIONS; DIAGNOSTIC RADIOGRAPHY; MEDICAL IMAGING; PLASTIC BOTTLES; POSITRON ANNIHILATION SPECTROSCOPY; REPAIR; RESTORATION; THERMOGRAPHY (TEMPERATURE MEASUREMENT); TOMOGRAPHY;

BASIS FUNCTIONS; DYNAMIC PET; ILL-POSED PROBLEMS; POSITRON EMISSION TOMOGRAPHY (PET); TOMOGRAPHIC RECONSTRUCTIONS;

POSITRON EMISSION TOMOGRAPHY;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; CLUSTER ANALYSIS; COMPUTER SIMULATION; FEEDBACK SYSTEM; FOURIER ANALYSIS; HUMAN; INFORMATION RETRIEVAL; KIDNEY; LIVER; METHODOLOGY; POSITRON EMISSION TOMOGRAPHY; SCINTISCANNING; SIGNAL PROCESSING; STATISTICAL ANALYSIS; THREE DIMENSIONAL IMAGING; TIME;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; CLUSTER ANALYSIS; COMPUTER SIMULATION; DATA INTERPRETATION, STATISTICAL; FEEDBACK; FOURIER ANALYSIS; HUMANS; IMAGING, THREE-DIMENSIONAL; INFORMATION STORAGE AND RETRIEVAL; KIDNEY; LIVER; PATTERN RECOGNITION, AUTOMATED; POSITRON-EMISSION TOMOGRAPHY; SIGNAL PROCESSING, COMPUTER-ASSISTED; TIME FACTORS;

EID: 46349085974     PISSN: 02780062     EISSN: None     Source Type: Journal    
DOI: 10.1109/TMI.2008.923698     Document Type: Article

References (63)

1. 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.
2. R. M. Lewitt and S. Matej, "Overview of methods for image reconstruction from projections in emission computed tomography," Proc. IEEE, vol. 91, no. 10, pp. 1588-1611, Oct. 2003.
3. J. Y. Qi and R. M. Leahy, "Iterative reconstruction techniques in emission computed tomography," Phys. Med. Biol., vol. 51, no. 15, pp. R541-R578, Aug. 2006.
4. T. Hebert and R. Leahy, "A generalized EM algorithm, for 3-D Bayesian reconstruction from poisson data using Gibbs priors," IEEE Trans. Med. Imag., vol. 8, no. 2, pp. 194-202, Jun. 1989.
5. J. A. Fessler, "Penalized weighted least-squares image-reconstruction for positron emission tomography," IEEE Trans. Med. Imag., vol. 13, no. 2, pp. 290-300, Jun. 1994.
6. J. A. Fessler, "Hybrid poisson/polynomial objective functions for tomographic image reconstruction from transmission scans," IEEE Trans. Image Process., vol. 4, no. 10, pp. 1439-1450, Oct. 1995.
7. T. E. Nichols, J. Qi, E. Asma, and R. M. Leahy, "Spatiotemporal reconstruction of list-mode PET data," IEEE Trans. Med. Imag., vol. 21, no. 4, pp. 396-404, Apr. 2002.
8. Q. Li, E. Asma, S. Ahn, and R. M. Leahy, "A fast fully 4-D incremental gradient reconstruction algorithm for list mode PET data," IEEE Trans. Med. Imag., vol. 26, no. 1, pp. 58-67, Jan. 2007.
9. J. Verhaeghe, Y. D'Asseler, S. Vandenberghe, S. Staelens, and I. Lemahieu, "An investigation of temporal regularization techniques for dynamic PET reconstructions using temporal splines," Med. Phys., vol. 34, no. 5, pp. 1525-1875, May 2007.
10. N. M. Alpert, A. Reilhac, T. C. Chio, and I. Selesnick, "Optimization of dynamic measurement of receptor kinetics by wavelet denoising," NeuroImage, vol. 30, no. 2, pp. 444-451, Apr. 2006.
11. P. Millet, V. Ibanez, J. Delforge, S. Pappata, and J. Guimon, "Wavelet analysis of dynamic PET data: Application to the parametric imaging of benzodiazepine receptor concentration," NeuroImage, vol. 11, no. 5, pp. 458-472, May 2000.
12. F. E. Turkheimer, M. Brett, D. Visvikis, and V. J. Cunningham, "Multiresolution analysis of emission tomography images in the wavelet domain," J. Cereb. Blood Flow Metab., vol. 19, no. 11, pp. 1189-1208, Nov. 1999.
13. D. L. Donoho, "Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition," Appl. Computational Harmonic Anal., vol. 2, no. 2, pp. 101-126, Apr. 1995.
14. E. D. Kolaczyk, "A wavelet shrinkage approach to tomographic image reconstruction," J. Am. Stat. Assoc., vol. 91, no. 435, pp. 1079-1090, Sep. 1996.
15. F. Abramovich and B. W. Silverman, "Wavelet decomposition approaches to statistical inverse problems," Biometrika, vol. 85, no. 1, pp. 115-129, Mar. 1998.
16. D. L. Donoho, "De-noising by soft-thresholding," IEEE Trans. Inf. Theory, vol. 41, no. 3, pp. 613-627, May 1995.
17. J. L. Starck, M. K. Nguyen, and F. Murtagh, "Wavelets and curvelets for image deconvolution: A combined approach," Signal Process., vol. 83, no. 10, pp. 2279-2283, Oct. 2003.
18. M. A. T. Figueiredo and R. D. Nowak, "An EM algorithm, for wavelet-based image restoration," IEEE Trans. Image Process., vol. 12, no. 8, pp. 906-916, Aug. 2003.
19. T. Frese, C. A. Bouman, and K. Sauer, "Adaptive wavelet graph model for bayesian tomographic reconstruction," IEEE Trans. Image Process., vol. 11, no. 7, pp. 756-770, Jul. 2002.
20. R. D. Nowak and E. D. Kolaczyk, "A statistical multiscale framework for poisson inverse problems," IEEE Trans. Inf. Theory, vol. 46, no. 5, pp. 1811-1825, Aug. 2000.
21. I. Khalidov and M. Unser, "From differential equations to the construction of new wavelet-like bases," IEEE Trans. Signal Process., vol. 54, no. 4, pp. 1256-1267, Apr. 2006.
22. D. L. Snyder, "Parameter estimation for dynamic studies in emission, tomography systems having list-mode data," IEEE Trans. Nucl. Sci., vol. NS-31, no. 2, pp. 925-931, 1984.
23. B. W. Reutter, G. T. Gullberg, and R. H. Huesman, "Direct leastsquares estimation of spatiotemporal distributions from dynamic SPECT projections using a spatial segmentation and temporal B-splines," IEEE Trans. Med. Imag., vol. 19, no. 5, pp. 434-450, May 2000.
24. A. J. Reader, F. C. Sureau, C. Comtat, R. Trebossen, and I. Buvat, "Joint estimation of dynamic PET images and temporal basis functions using fully 4D ML-EM," Phys. Med. Biol., vol. 51, no. 21, pp. 5455-5474, Nov. 2006.
25. J. Matthews, D. Bailey, P. Price, and V. Cunningham, "The direct calculation of parametric images from dynamic PET data using maximumlikelihood iterative reconstruction," Phys. Med. Biol., vol. 42, no. 6, pp. 1155-1173, 1997.
26. Y. S. Xu, J. B. Weaver, D. M. Healy, and J. Lu, "Wavelet transform domain filters - A spatially selective noise filtration technique," IEEE Trans. Image Process., vol. 3, no. 6, pp. 747-758, Nov. 1994.
27. M. Unser and A. Aldroubi, "A review of wavelets in biomedical applications," Proc. IEEE, vol. 84, no. 4, pp. 626-638, Apr. 1996.
28. D. L. Donoho and X. M. Huo, "Uncertainty principles and ideal atomic decomposition," IEEE Trans. Inf. Theory, vol. 47, no. 7, pp. 2845-2862, Nov. 2001.
29. S. G. Mallat, "A theory for multiresolution signal decomposition: The wavelet representation," IEEE Trans. Pattern Anal. Mach. Intell., vol. 11, no. 7, pp. 674-693, Jul. 1989.
30. M. Unser and T. Blu, "Wavelet theory demystified," IEEE Trans. Signal Process., vol. 51, no. 2, pp. 470-483, Feb. 2003.
31. M. Unser and T. Blu, "Cardinal exponential splines: Part I - Theory and filtering algorithms," IEEE Trans. Signal Process., vol. 53, no. 4, pp. 1425-1438, Apr. 2005.
32. M. Unser, "Cardinal exponential splines: Part II-Think analog, act digital," IEEE Trans. Signal Process., vol. 53, no. 4, pp. 1439-1449, Apr. 2005.
33. S. R. Cherry, J. A. Sorensen, and M. E. Phelps, Physics in Nuclear-Medicine, 3rd ed. Philadelphia, PA: Saunders, 2003, ch. 20, pp. 377-403.
34. R. N. Gunn, S. R. Gunn, and V. J. Cunningham, "Positron emission tomography compartmental models," J. Cereb. Blood Flow Metab., vol. 21, no. 6, pp. 635-652, Jun. 2001.
35. M. Slifstein and M. Lamelle, "Models and methods for derivation of in vivo neuroreceptor parameters with PET and SPECT reversible radio-tracers," Nucl. Med. Biol., vol. 28, no. 5, pp. 595-608, Jul. 2001.
36. M. Bentourkia and H. Zaidi, Quantitative Analysis in Nuclear Medicine Imaging. New York: Springer, 2006, ch. 12, pp. 391-413.
37. 14C] deoxyglucose method for measurement of local cerebral glucoseutilization-Theory, procedure, and normal values in conscious and anesthetized albinorat," J. Neurochem., vol. 28, no. 5, pp. 897-916, 1977.
38. M. E. Phelps, S. C. Huang, E. J. Hoffman, C. Selin, L. Sokoloff, and D. E. Kuhl, "Tomographic measurement of local cerebral glucose metabolic-rate in humans with (F-18)2-Fluoro-2-Deoxy-D-Glucose-validation of method," Ann. Neurol., vol. 6, no. 5, pp. 371-388, 1979.
39. M. C. Asselin, L. M. Wahl, V. J. Cunningham, S. Amano, and C. Nahmias, "In vivo metabolism and partitioning of 6-[F-18]fluoro-1-metatyrosine in whole blood: A unified compartment model," Phys. Med. Biol., vol. 47, no. 11, pp. 1961-1977, Jun. 2002.
40. R. Davenport, "The derivation of the gamma-variate relationship for tracer dilution curves," J. Nucl. Med., vol. 24, no. 10, pp. 945-948, 1983.
41. D. Feng, S. C. Huang, and X. M. Wang, "Models for computersimulation studies of input functions for tracer kinetic modeling with positron emission tomography," Int. J. Bio-Med. Comput., vol. 32, no. 2, pp. 95-110, Mar. 1993.
42. M. M. Graham, "Physiologic smoothing of blood time-activity curves for PET data analysis," J. Nucl. Med., vol. 38, no. 7, pp. 1161-1168, Jul. 1997.
43. S. R. Golish, J. D. Hove, H. R. Schelbert, and S. S. Gambhir, "A fast nonlinear method for parametric imaging of myocardial perfusion by dynamic N-13-ammonia PET," J. Nucl. Med., vol. 42, no. 6, pp. 924-931, 2001.
44. J. A. Thompson, F. Starmar, R. E. Whalen, and H. D. McIntosh, "Indicator transit time considered as a gamma variate," Cire. Res., vol. 14, pp. 502-515, 1964.
45. D. L. Donoho and I. M. Johnstone, "Adapting to unknown smoothness via wavelet shrinkage," J. Am. Stat. Assoc., vol. 90, no. 432, pp. 1200-1224, Dec. 1995.
46. A. Chambolle, R. A. DeVore, N. Y. Lee, and B. J. Lucier, "Non-linear wavelet image processing: Variational problems, compression, and noise removal through wavelet shrinkage," IEEE Trans. Image Process., vol. 7, no. 3, pp. 319-335, Mar. 1998.
47. M. Unser and A. Aldroubi, "A general sampling theory for nonideal acquisition devices," IEEE Trans. Signal Process., vol. 42, no. 11, pp. 2915-2925, Nov. 1994.
48. P. Millet, C. Graf, A. Buck, B. Walder, and V. Ibanez, "Evaluation of the reference tissue models for PET and SPECT benzodiazepine binding parameters," NeuroImage, vol. 17, no. 2, pp. 928-942, Oct. 2002.
49. W. P. Segars, D. S. Lalush, and B. M. W. Tsui, "A realistic spline-based dynamic heart phantom," IEEE Trans. Nucl. Sci., vol. 46, no. 3, pp. 503-506, Jun. 1999.
50. I. G. Zubal, C. R. Harrell, E. O. Smith, Z. Rattner, G. Gindi, and P. B. Hoffer, "Computerized 3-dimensional segmented human anatomy," Med. Phys., vol. 21, no. 2, pp. 299-302, Feb. 1994.
51. J. Delforge, S. Pappata, P. Millet, Y. Samson, B. Bendriem, A. Jobert, C. Crouzel, and A. Syrota, "Quantification of benzodiazepine receptors in human brain using PET, [C-11] flumazenil, and a single-experiment protocol," J. Cereb. Blood Flow Metab., vol. 15, no. 2, pp. 284-300, Mar. 1995.
52. S. Surti and J. S. Karp, "Imaging characteristics of a 3-dimensional GSO whole-body PET camera," J. Nucl. Med., vol. 45, no. 6, pp. 1040-1049, 2004.
53. M. E. Daube-Witherspoon and G. Muehllehner, "Treatment of axial data in 3-dimensional PET," J. Nucl. Med., vol. 28, no. 11, pp. 1717-1724, Nov. 1987.
54. M. Brambilla, C. Secco, M. Dominietto, R. Matheoud, G. Sacchetti, and E. Inglese, "Performance characteristics obtained for a new 3-dimensional lutetium oxylorthosilicate-based whole-body PET/CT scanner with the national electrical manufacturers association NU 2-2001 standard," J. Nucl. Med., vol. 46, no. 12, pp. 2083-2091, Dec. 2005.
55. J. P. J. Carney, D. W. Townsend, V. Rappoport, and B. Bendriem, "Method for transforming ct images for attenuation correction in pet/ct imaging," Med. Phys., vol. 33, no. 4, pp. 976-983, Apr. 2006.
56. I. Loris, G. Nolet, I. Daubechies, and F. Dahlen, "Tomographic inversion using 11-normregularization of wavelet coefficients," Geophys. J. Int., vol. 170, no. 1, pp. 359-370, Jul. 2007.
57. B. W. Silverman, M. C. Jones, J. D. Wilson, and D. W. Nychka, "A smoothed EM approach to indirect estimation problems, with particular reference to stereology and emission tomography," J. R. Stat. Soc. Series B-Methodological, vol. 52, no. 2, pp. 271-324, 1990.
58. J. Llacer, E. Veklerov, K. J. Coakley, E. J. Hoffman, and J. Nunez, "Statistical-analysis of maximum-likelihood estimator images of human brain FDG PET studies," IEEE Trans. Med. Imag., vol. 12, no. 2, pp. 215-231, Jun. 1993.
59. E. T. P. Slijpen and F. J. Beekman, "Comparison of post-filtering and filtering between iterations for SPECT reconstruction," IEEE Trans. Nucl. Sci., vol. 46, no. 6, pp. 2233-2238, Dec. 1999.
60. S. G. Chang, B. Yu, and M. Vetterli, "Adaptive wavelet thresholding for image denoising and compression," IEEE Trans. Image Process., vol. 9, no. 9, pp. 1532-1546, Sep. 2000.
61. R. M. Lewitt, "Alternatives to voxels for image representation in iterative reconstruction algorithms," Phys. Med. Biol., vol. 37, no. 3, pp. 705-716, 1992.
62. S. Horbelt, M. Liebling, and M. Unser, "Discretization of the radon transform and of its inverse by spline convolutions," IEEE Trans. Med. Imag., vol. 21, no. 4, pp. 363-376, Apr. 2002.
63. S. Mallat, A Wavelet Tour of Signal Processing. San Diego, CA: Academic, 1998.