Fundamental relationship between the noise properties of grating-based differential phase contrast CT and absorption CT: Theoretical framework using a cascaded system model and experimental validation

Medical Physics

Volumn 40, Issue 2, 2013, Pages

  Li, Ke ^a   Bevins, Nicholas ^a   Zambelli, Joseph ^a   Chen, Guang Hong ^a,b  

^a UNIVERSITY OF WISCONSIN SCHOOL OF MEDICINE AND PUBLIC HEALTH   (United States)

^b UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

cone beam CT (CBCT); differential phase contrast CT (DPC CT); noise equivalent quanta (NEQ); noise power spectrum (NPS)

Indexed keywords

DATA ACQUISITION; INTERFEROMETERS; OPTICAL TRANSFER FUNCTION; POWER SPECTRUM; X RAYS;

CONE-BEAM COMPUTED TOMOGRAPHY; CONEBEAM CT; CONVENTIONAL ABSORPTION; DIFFERENTIAL PHASE CONTRAST; EXPERIMENTAL VALIDATIONS; GRATING INTERFEROMETERS; NOISE EQUIVALENT QUANTA; NOISE POWER SPECTRUM;

COMPUTERIZED TOMOGRAPHY;

ABSORPTION; ABSORPTION COMPUTER TOMOGRAPHY; ARTICLE; COMPUTER ASSISTED TOMOGRAPHY; CONCEPTUAL FRAMEWORK; CONE BEAM COMPUTED TOMOGRAPHY; DIFFERENTIAL PHASE CONTRAST COMPUTER TOMOGRAPHY; GRATING INTERFEROMETER; INFORMATION PROCESSING; INTERFEROMETER; MODULATION TRANSFER FUNCTION; NOISE; NOISE EQUIVALENT QUANTA; NOISE POWER SPECTRUM; POWER SPECTRUM; PRIORITY JOURNAL; RADIOLOGICAL PARAMETERS; THEORETICAL STUDY; X RAY CONE BEAM COMPUTED TOMOGRAPHY; IMAGE PROCESSING; INTERFEROMETRY; METHODOLOGY; REPRODUCIBILITY; SIGNAL NOISE RATIO; THEORETICAL MODEL;

ABSORPTION; CONE-BEAM COMPUTED TOMOGRAPHY; IMAGE PROCESSING, COMPUTER-ASSISTED; INTERFEROMETRY; MODELS, THEORETICAL; REPRODUCIBILITY OF RESULTS; SIGNAL-TO-NOISE RATIO;

EID: 84873588356     PISSN: 00942405     EISSN: None     Source Type: Journal    
DOI: 10.1118/1.4788647     Document Type: Article

References (73)

1. C. David, B. Nohammer, H. H. Solak, and E. Ziegler, " Differential x-ray phase contrast imaging using a shearing interferometer.," Appl. Phys. Lett. 81, 3287-3289 (2002). 10.1063/1.1516611
2. A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, " Demonstration of x-ray Talbot interferometry.," Jpn. J. Appl. Phys. 42, L866-L868 (2003). 10.1143/JJAP.42.L866
3. T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Zeigler, " X-ray phase imaging with a grating interferometer.," Opt. Express 13, 6296-6304 (2005). 10.1364/OPEX.13.006296
4. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, " Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources.," Nat. Phys. 2, 258-261 (2006). 10.1038/nphys265
5. C. Kottler, C. David, F. Pfeiffer, and O. Bunk, " A two-directional approach for grating based differential phase contrast imaging using hard x-rays.," Opt. Express 15, 1175-1181 (2007). 10.1364/OE.15.001175
6. M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. PFeiffer, O. Bunk, and C. David, " High resolution differential phase contrast imaging using a magnifying projection geometry with micro-focus x-ray source.," Appl. Phys. Lett. 90, 224101 (2007). 10.1063/1.2743928
7. A. Momose, W. Yashiro, H. Kuwabara, and K. Kawabata, " Grating-based x-ray phase imaging using multiline x-ray source.," Jpn. J. Appl. Phys. 48, 076512-1-076512-5 (2009). 10.1143/JJAP.48.076512
8. A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, " Phase tomography by x-ray Talbot interferometry for biological imaging.," Jpn. J. Appl. Phys. 45, 5254-5262 (2006). 10.1143/JJAP.45.5254
9. T. Weitkamp, C. David, C. Kottler, O. Bunk, and F. Pfeiffer, " Tomography with grating interferometers at low-brilliance sources.," Proc. SPIE 6318, 63180S (2006). 10.1117/12.683851
10. F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, " High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography.," Phys. Med. Biol. 52, 6923-6930 (2007). 10.1088/0031-9155/52/23/010
11. F. Pfeiffer, C. Kottler, O. Bunk, and C. David, " Hard x-ray phase tomography with low-brilliance sources.," Phys. Rev. Lett. 98, 108105 (2007). 10.1103/PhysRevLett.98.108105
12. A. Momose, W. Yashiro, H. Maikusa, and Y. Takeda, " High-speed x-ray phase imaging and x-ray phase tomography with Talbot interferometer and white synchrotron radiation.," Opt. Express 17, 12540-12545 (2009). 10.1364/OE.17.012540
13. M. Bech, T. Jensen, R. Feidenhans'l, O. Bunk, C. David, and F. Pfeiffer, " Soft-tissue phase-contrast tomography with an x-ray tube source.," Phys. Med. Biol. 54, 2747-2753 (2009). 10.1088/0031-9155/54/9/010
14. T. Donath, F. Pfeiffer, O. Bunk, C. Gruenzweig, E. Hempel, S. Popescu, P. Vock, and C. David, " Toward clinical x-ray phase-contrast CT demonstration of enhanced soft-tissue contrast in human specimen.," Invest. Radiol. 45, 445-452 (2010). 10.1097/RLI.0b013e3181e21866
15. J. Zambelli, N. Bevins, Z. Qi, and G.-H. Chen, " Radiation dose efficiency comparison between differential phase contrast CT and conventional absorption CT.," Med. Phys. 37, 2473-2479 (2010). 10.1118/1.3425785
16. Z. Qi, J. Zambelli, N. Bevins, and G.-H. Chen, " Quantitative imaging of electron density and effective atomic number using phase contrast CT.," Phys. Med. Biol. 55, 2669-2677 (2010). 10.1088/0031-9155/55/9/016
17. E. Nickoloff and R. Riley, " A simplified approach for modulation transfer function determinations in computed tomography.," Med. Phys. 12, 437-442 (1985). 10.1118/1.595706
18. International Commission in Radiation Units and Measurements, " Medical imaging: The assessment of image quality.," ICRU Report No. 54 (ICRU Publications, Bethesda, MD, 1996).
19. Handbook of Medical Imaging, Volume 1. Physics and Psychophysics, 1st ed., edited by, J. Beutel, H. Kundel, and, R. Van Metter, (SPIE, Bellingham, Washington, 2000).
20. J. H. Siewerdsen, I. A. Cunningham, and D. A. Jaffray, " A framework for noise-power spectrum analysis of multidimensional images.," Med. Phys. 29, 2655-2671 (2002). 10.1118/1.1513158
21. K. L. Boedeker, V. N. Cooper, and M. F. McNitt-Gray, " Application of the noise power spectrum in modern diagnostic MDCT: Part I. Measurement of noise power spectra and noise equivalent quanta.," Phys. Med. Biol. 52, 4027-4046 (2007). 10.1088/0031-9155/52/14/002
22. K. L. Boedeker and M. F. McNitt-Gray, " Application of the noise power spectrum in modern diagnostic MDCT: Part II. Noise power spectra and signal to noise.," Phys. Med. Biol. 52, 4047-4061 (2007). 10.1088/0031-9155/52/14/003
23. D. Tward and J. Siewerdsen, " Cascaded systems analysis of the 3D noise transfer characteristics of flat-panel cone-beam CT.," Med. Phys. 35, 5510-5529 (2008). 10.1118/1.3002414
24. D. J. Tward and J. H. Siewerdsen, " Noise aliasing and the 3D NEQ of flat-panel cone-beam CT: Effect of 2D/3D apertures and sampling.," Med. Phys. 36, 3830-3843 (2009). 10.1118/1.3166933
25. R. Raupach and T. Flohr, " Analytical evaluation of the signal and noise propagation in x-ray differential phase-contrast computed tomography.," Phys. Med. Biol. 56, 2219-2244 (2011). 10.1088/0031-9155/56/ 7/020
26. G.-H. Chen, J. Zambelli, K. Li, N. Bevins, and Z. Qi, " Scaling law for noise variance and spatial resolution in differential phase contrast computed tomography.," Med. Phys. 38, 584-588 (2011). 10.1118/1.3533718
27. T. Köhler, K. J. Engel, and E. Roessl, " Noise properties of grating-based x-ray phase contrast computed tomography.," Med. Phys. 38, S106-S116 (2011). 10.1118/1.3532396
28. X. Tang, Y. Yang, and S. Tang, " Characterization of imaging performance in differential phase contrast CT compared with the conventional CT-noise power spectrum NPS(k).," Med. Phys. 38, 4386-4395 (2011). 10.1118/1.3602071
29. H. Barrett, S. Gordon, and R. Hershel, " Statistical limitations in transaxial tomography.," Comput. Biol. Med 6, 307-323 (1976). 10.1016/0010-4825(76)90068-8
30. J. Zambelli, K. Li, N. Bevins, Z. Qi, and G. Chen, " Noise characteristics of x-ray differential phase contrast CT.," Proc. SPIE 7961, 79613N (2011). 10.1117/12.878497
31. K. Li, N. Bevins, J. Zambelli, Z. Qi, and G.-H. Chen, " Detection performance study for cone-beam differential phase contrast CT.," Proc. SPIE 8313, 83131L (2012). 10.1117/12.911593
32. A. E. Burgess, F. L. Jacobson, and P. F. Judy, " Human observer detection experiments with mammograms and power-law noise.," Med. Phys. 28, 419-437 (2001). 10.1118/1.1355308
33. X. Gong, S. J. Glick, B. Liu, A. A. Vedula, and S. Thacker, " A computer simulation study comparing lesion detection accuracy with digital mammography, breast tomosynthesis, and cone-beam CT breast imaging.," Med. Phys. 33, 1041-1052 (2006). 10.1118/1.2174127
34. K. G. Metheany, C. K. Abbey, N. Packard, and J. M. Boone, " Characterizing anatomical variability in breast CT images.," Med. Phys. 35, 4685-4694 (2008). 10.1118/1.2977772
35. G. J. Gang, D. J. Tward, J. Lee, and J. H. Siewerdsen, " Anatomical background and generalized detectability in tomosynthesis and cone-beam CT.," Med. Phys. 37, 1948-1965 (2010). 10.1118/1.3352586
36. G. J. Gang, J. Lee, J. W. Stayman, D. J. Tward, W. Zbijewski, J. L. Prince, and J. H. Siewerdsen, " Analysis of Fourier-domain task-based detectability index in tomosynthesis and cone-beam CT in relation to human observer performance.," Med. Phys. 38, 1754-1768 (2011). 10.1118/1.3560428
37. L. Chen, C. K. Abbey, A. Nosrateih, K. K. Lindfors, and J. M. Boone, " Anatomical complexity in breast parenchyma and its implications for optimal breast imaging strategies.," Med. Phys. 39, 1435-1441 (2012). 10.1118/1.3685462
38. I. Reiser, R. M. Nishikawa, M. L. Giger, J. M. Boone, K. K. Lindfors, and K. Yang, " Automated detection of mass lesions in dedicated breast CT: A preliminary study.," Med. Phys. 39, 866-873 (2012). 10.1118/1.3678991
39. X. Tang, Y. Yang, and S. Tang, " Imaging performance in differential phase contrast CT compared with the conventional CT-noise equivalent quanta NEQ(k).," Proc. SPIE 8313, 83132I (2012). 10.1117/12.911420
40. X. Tang, Y. Yang, and S. Tang, " Characterization of imaging performance in differential phase contrast CT compared with the conventional CT: Spectrum of noise equivalent quanta NEQ(k).," Med. Phys. 39, 4467-4482 (2012). 10.1118/1.4730287
41. S. J. Riederer, N. J. Pelc, and D. A. Chesler, " The noise power spectrum in computed x-ray tomograhy.," Phys. Med. Biol. 23, 446-454 (1978). 10.1088/0031-9155/23/3/008
42. R. F. Wagner, D. G. Brown, and M. S. Pastel, " Application of information theory to the assessment of computed tomography.," Med. Phys. 6, 83-94 (1979). 10.1118/1.594559
43. K. Hanson, " Detectability in computed tomographic images.," Med. Phys. 6, 441-451 (1979). 10.1118/1.594534
44. M. F. Kijewski and P. F. Judy, " The noise power spectrum of CT images.," Phys. Med. Biol. 32, 565-575 (1987). 10.1088/0031-9155/32/5/003
45. I. A. Cunningham and R. Shaw, " Signal-to-noise optimization of medical imaging systems.," J. Opt. Soc. Am. A 16, 621-632 (1999). 10.1364/JOSAA.16.000621
46. M. Rabbani, R. Shaw, and R. V. Metter, " Detective quantum efficiency of imaging systems with amplifying and scattering mechanisms.," J. Opt. Soc. Am. A 4, 895-901 (1987). 10.1364/JOSAA.4.000895
47. I. A. Cunningham, M. S. Westmore, and A. Fenster, " A spatial-frequency dependent quantum accounting diagram and detective quantum efficiency model of signal and noise propagation in cascaded imaging systems.," Med. Phys. 21, 417-427 (1994). 10.1118/1.597401
48. J. Yao and I. A. Cunningham, " Parallel cascades: New ways to describe noise transfer in medical imaging systems.," Med. Phys. 28, 2020-2038 (2001). 10.1118/1.1405842
49. J. H. Siewerdsen, L. E. Antonuk, Y. El-Mohri, J. Yorkston, W. Huang, J. M. Boudry, and I. A. Cunningham, " Empirical and theoretical investigation of the noise performance of indirect detection, active matrix flat-panel imagers (AMFPIs) for diagnostic radiology.," Med. Phys. 24, 71-89 (1997). 10.1118/1.597919
50. J.-P. Bissonnette, I. A. Cunningham, D. A. Jaffray, A. Fenster, and P. Munro, " A quantum accounting and detective quantum efficiency analysis for video-based portal imaging.," Med. Phys. 24, 815-826 (1997). 10.1118/1.598009
51. J. Siewerdsen, L. Antonuk, Y. El-Mohri, J. Yorkston, W. Huang, and I. Cunningham, " Signal, noise power spectrum, and detective quantum efficiency of indirect-detection flat-panel imagers for diagnostic radiology.," Med. Phys. 25, 614-628 (1998). 10.1118/1.598243
52. D. G. Drake, D. A. Jaffray, and J. W. Wong, " Characterization of a fluoroscopic imaging system for kV and MV radiography.," Med. Phys. 27, 898-905 (2000). 10.1118/1.598955
53. W. Zhao, W. G. Ji, and J. A. Rowlands, " Effects of characteristic x rays on the noise power spectra and detective quantum efficiency of photoconductive x-ray detectors.," Med. Phys. 28, 2039-2049 (2001). 10.1118/1.1405845
54. A. Ganguly, S. Rudin, D. R. Bednarek, and K. R. Hoffmann, " Micro-angiography for neuro-vascular imaging. II. Cascade model analysis.," Med. Phys. 30, 3029-3039 (2003). 10.1118/1.1617550
55. S. Vedantham, A. Karellas, and S. Suryanarayanan, " Solid-state fluoroscopic imager for high-resolution angiography: Parallel-cascaded linear systems analysis.," Med. Phys. 31, 1258-1268 (2004). 10.1118/1.1689014
56. S. Richard and J. H. Siewerdsen, " Cascaded systems analysis of noise reduction algorithms in dual-energy imaging.," Med. Phys. 35, 586-601 (2008). 10.1118/1.2826556
57. P. Prakash, W. Zbijewski, G. J. Gang, Y. Ding, J. W. Stayman, J. Yorkston, J. A. Carrino, and J. H. Siewerdsen, " Task-based modeling and optimization of a cone-beam CT scanner for musculoskeletal imaging.," Med. Phys. 38, 5612-5629 (2011). 10.1118/1.3633937
58. C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzwrig, and C. David, " Grating interferometer based scanning setup for hard x-ray phase contrast imaging.," Rev. Sci. Instrum. 78, 043710 (2007). 10.1063/1.2723064
59. J. H. Siewerdsen and D. A. Jaffray, " Optimization of x-ray imaging geometry (with specific application to flat-panel cone-beam computed tomography).," Med. Phys. 27, 1903-1914 (2000). 10.1118/1.1286590
60. I. S. Kyprianou, S. Rudin, D. R. Bednarek, and K. R. Hoffmann, " Generalizing the MTF and DQE to include x-ray scatter and focal spot unsharpness: Application to a new microangiographic system.," Med. Phys. 32, 613-626 (2005). 10.1118/1.1844151
61. L. A. Feldkamp, L. C. Davis, and J. W. Kress, " Practical cone-beam algorithm.," J. Opt. Soc. Am. A 1, 612-619 (1984). 10.1364/JOSAA.1.000612
62. G. Faris and R. Byer, " Three-dimensional beam-deflection optical tomography of a supersonic jet.," Appl. Opt. 27, 5202-5212 (1988). 10.1364/AO.27.005202
63. Z. Huang, K. Kang, Z. Li, P. Zhu, Q. Yuan, W. Huang, J. Wang, and A. Yu, " Direct computed tomographic reconstruction for directional-derivative projections of computed tomography of diffraction enhanced imaging.," Appl. Phys. Lett. 89, 041124 (2006). 10.1063/1.2219405
64. Z. Qi and G.-H. Chen, " Direct fan-beam reconstruction algorithm via filtered backprojection for differential phase-contrast computed tomography.," X-Ray Opt. Instrum. 2008, 835172 (2008). 10.1155/2008/835172
65. K. Li, N. Bevins, J. Zambelli, and G.-H. Chen, " A new image reconstruction method to improve noise properties in x-ray differential phase contrast computed tomography.," Proc. SPIE 8313, 83131V (2012). 10.1117/12.911604
66. S. R. Deans, The Radon Transform and Some of Its Applications (Wiley, New York, 1983).
67. C. J. Bischof and J. C. Ehrhardt, " Modulation transfer function of the EMI CT head scanner.," Med. Phys. 4, 163-167 (1977). 10.1118/1.594305
68. J. Boone, " Determination of the presampled MTF in computed tomography.," Med. Phys. 28, 356-360 (2001). 10.1118/1.1350438
69. R. Raupach and T. Flohr, " Performance evaluation of x-ray differential phase contrast computed tomography (PCT) with respect to medical imaging.," Med. Phys. 39, 4761-4774 (2012). 10.1118/1.4736529
70. G.-H. Chen, N. Bevins, J. Zambelli, and Z. Qi, " Small-angle scattering computed tomography (SAS-CT) using a Talbot-Lau interferometer and a rotating anode x-ray tube: Theory and experiments.," Opt. Express 18, 12960-12970 (2010). 10.1364/OE.18.012960
71. J. Baek and N. J. Pelc, " The noise power spectrum in CT with direct fan beam reconstruction.," Med. Phys. 37, 2074-2081 (2010). 10.1118/1.3378673
72. J. Baek and N. J. Pelc, " Local and global 3D noise power spectrum in cone-beam CT system with FDK reconstruction.," Med. Phys. 38, 2122-2131 (2011). 10.1118/1.3556590
73. A. R. Pineda, D. J. Tward, A. Gonzalez, and J. H. Siewerdsen, " Beyond noise power in 3D computed tomography: The local NPS and off-diagonal elements of the Fourier domain covariance matrix.," Med. Phys. 39, 3240-3252 (2012). 10.1118/1.4705354