CT Image Quality Characterization

  • Ke Li
  • Guang-Hong ChenEmail author


This chapter presents mathematical and physics foundations of quantitative CT image quality assessment. The linear systems theory was applied to derive quantitative relations between noise, spatial resolution, and CT number of an idealized linear CT system and the associated hardware specifications, acquisition, and reconstruction parameters. The derivations not only highlighted the physical and mathematical foundations of several widely recognized image quality “laws” (e.g., the inverse scaling law between CT noise variance and radiation exposure level) but also the underlying assumptions behind these laws. Next, the chapter showed how these assumptions can be violated in realistic modern CT systems, even for those employing the linear filtered backprojection (FBP) algorithm. It demonstrated how the classical image quality models can be revised for modern systems. One revision is the introduction of a virtual image object with negative attenuation to compensate for the spatially and directionally varying impacts of the bowtie filter to CT noise power spectrum (NPS). After its revision, linear systems theory can still be used to model CT image quality of FBP-based realistic CT systems. Finally, the chapter demonstrated severe violations of the classical linear systems theory in CT systems with nonlinear model-based iterative reconstruction (MBIR) algorithms and the new challenges in estimating image quality properties for these systems. The chapter presented strategies toward addressing these challenges, including ensemble statistics- and task-based image quality assessment methods as well as empirical modeling of the relationship between image quality performance and system parameters. It also clarified the concept of NPS and justified the applicability of this objective image quality metric in nonlinear MBIR-based systems with nonstationary noise. Throughout this chapter, discussion on the topic of CT image quality was accompanied by illustrations and plots of experimental data, some of which are published for the first time.


Image quality Spatial resolution MTF CT noise Noise power spectrum CT number bias Linear systems theory Model-based iterative reconstruction (MBIR) 


  1. 1.
    Verdun FR, Racine D, Ott JG, Tapiovaara MJ, Toroi P, Bochud FO, et al. Image quality in CT: from physical measurements to model observers. Phys Med. 2015;31(8):823–43.CrossRefGoogle Scholar
  2. 2.
    Goldman LW. Principles of CT: radiation dose and image quality. J Nucl Med Technol. 2007;35(4):213–25; quiz 26–8. Epub 2007/11/17.PubMedCrossRefPubMedCentralGoogle Scholar
  3. 3.
    Radiology ACo. CT Accreditation Program Requirements. 2018.Google Scholar
  4. 4.
    Radiology ACo. CT Accreditation Program Testing Instructions. 2018.Google Scholar
  5. 5.
    #2 DX-RICTG. AAPM Report No. 39 Specification and acceptance testing of computed tomography scanners. AAPM, 1993.Google Scholar
  6. 6.
    #12 DX-rICTG. AAPM Report No. 74 Quality control in diagnostic radiology. 2002.Google Scholar
  7. 7.
    Sauer K, Bouman C. A local update strategy for iterative reconstruction from projections. Ieee T Signal Process. 1993;41(2):534–48.CrossRefGoogle Scholar
  8. 8.
    Fessler JA, Hero AO. Penalized maximum-likelihood image-reconstruction using space-alternating generalized Em algorithms. Ieee T Image Process. 1995;4(10):1417–29.CrossRefGoogle Scholar
  9. 9.
    Lange K, Fessler JA. Globally convergent algorithms for maximum a-posteriori transmission tomography. Ieee T Image Process. 1995;4(10):1430–8.CrossRefGoogle Scholar
  10. 10.
    Bouman CA, Sauer K. A unified approach to statistical tomography using coordinate descent optimization. Ieee T Image Process. 1996;5(3):480–92.CrossRefGoogle Scholar
  11. 11.
    Thibault JB, Sauer KD, Bouman CA, Hsieh J. A three-dimensional statistical approach to improved image quality for multislice helical CT. Med Phys. 2007;34(11):4526–44.CrossRefGoogle Scholar
  12. 12.
    Chen GH, Tang J, Leng SH. Prior image constrained compressed sensing (PICCS): a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets. Med Phys. 2008;35(2):660–3.PubMedPubMedCentralCrossRefGoogle Scholar
  13. 13.
    Lauzier PT, Chen GH. Characterization of statistical prior image constrained compressed sensing. I. Applications to time-resolved contrast-enhanced CT. Med Phys. 2012;39(10):5930–48.PubMedPubMedCentralCrossRefGoogle Scholar
  14. 14.
    Yu Z, Thibault JB, Bouman CA, Sauer KD, Hsieh JA. Fast model-based X-ray CT reconstruction using spatially nonhomogeneous ICD optimization. Ieee T Image Process. 2011;20(1):161–75.CrossRefGoogle Scholar
  15. 15.
    Pickhardt PJ, Lubner MG, Kim DH, Tang J, Ruma JA, del Rio AM, et al. Abdominal CT with model-based iterative reconstruction (MBIR): initial results of a prospective trial comparing ultralow-dose with standard-dose imaging. Am J Roentgenol. 2012;199(6):1266–74.CrossRefGoogle Scholar
  16. 16.
    Yasaka K, Katsura M, Akahane M, Sato J, Matsuda I, Ohtomo K. Model-based iterative reconstruction for reduction of radiation dose in abdominopelvic CT: comparison to adaptive statistical iterative reconstruction. Springerplus. 2013;2:209.PubMedPubMedCentralCrossRefGoogle Scholar
  17. 17.
    Smith EA, Dillman JR, Goodsitt MM, Christodoulou EG, Keshavarzi N, Strouse PJ. Model-based iterative reconstruction: effect on patient radiation dose and image quality in pediatric body CT. Radiology. 2014;270(2):526–34.PubMedPubMedCentralCrossRefGoogle Scholar
  18. 18.
    Richard S, Husarik DB, Yadava G, Murphy SN, Samei E. Towards task-based assessment of CT performance: system and object MTF across different reconstruction algorithms. Med Phys. 2012;39(7):4115–22.PubMedPubMedCentralCrossRefGoogle Scholar
  19. 19.
    Pal D, Kulkarni S, Yadava G, Thibault JB, Sauer K, Hsieh J. Analysis of noise power spectrum for linear and non-linear reconstruction algorithms for CT. 2011 Ieee Nuclear Science Symposium and Medical Imaging Conference (Nss/Mic). 2011:4382–5.Google Scholar
  20. 20.
    Li K, Tang J, Chen GH. Statistical model based iterative reconstruction (MBIR) in clinical CT systems: experimental assessment of noise performance. Med Phys. 2014;41(4):041906.. Epub 2014/04/04PubMedPubMedCentralCrossRefGoogle Scholar
  21. 21.
    Li K, Garrett J, Ge Y, Chen GH. Statistical model based iterative reconstruction (MBIR) in clinical CT systems. Part II. Experimental assessment of spatial resolution performance. Med Phys. 2014;41(7):071911.. Epub 2014/07/06PubMedPubMedCentralCrossRefGoogle Scholar
  22. 22.
    Li K, Gomez-Cardona D, Hsieh J, Lubner MG, Pickhardt PJ, Chen GH. Statistical model based iterative reconstruction in clinical CT systems. Part III. Task-based kV/mAs optimization for radiation dose reduction. Med Phys. 2015;42(9):5209–21.PubMedPubMedCentralCrossRefGoogle Scholar
  23. 23.
    Solomon J, Samei E. Are uniform phantoms sufficient to characterize the performance of iterative reconstruction in CT? Medical Imaging 2013: Physics of Medical Imaging. 2013;8668.Google Scholar
  24. 24.
    Solomon J, Mileto A, Ramirez-Giraldo JC, Samei E. Diagnostic performance of an advanced modeled iterative reconstruction algorithm for low-contrast detectability with a third-generation dual-source multidetector CT scanner: potential for radiation dose reduction in a multireader study. Radiology. 2015;275(3):735–45.PubMedPubMedCentralCrossRefGoogle Scholar
  25. 25.
    Yu LF, Vrieze TJ, Leng S, Fletcher JG, McCollough CH. Technical note: measuring contrast- and noise-dependent spatial resolution of an iterative reconstruction method in CT using ensemble averaging. Med Phys. 2015;42(5):2261–7.PubMedPubMedCentralCrossRefGoogle Scholar
  26. 26.
    Chen BY, Christianson O, Wilson JM, Samei E. Assessment of volumetric noise and resolution performance for linear and nonlinear CT reconstruction methods. Med Phys. 2014;41(7):071909.PubMedPubMedCentralCrossRefGoogle Scholar
  27. 27.
    Chen BY, Giraldo JCR, Solomon J, Samei E. Evaluating iterative reconstruction performance in computed tomography. Med Phys. 2014;41(12):121913.PubMedCrossRefPubMedCentralGoogle Scholar
  28. 28.
    Solomon J, Samei E. Quantum noise properties of CT images with anatomical textured backgrounds across reconstruction algorithms: FBP and SAFIRE. Med Phys. 2014;41(9):091908.CrossRefGoogle Scholar
  29. 29.
    Vaishnav JY, Jung WC, Popescu LM, Zeng R, Myers KJ. Objective assessment of image quality and dose reduction in CT iterative reconstruction. Med Phys. 2014;41(7):071904.PubMedCrossRefPubMedCentralGoogle Scholar
  30. 30.
    Gang GJ, Stayman JW, Zbijewski W, Siewerdsen JH. Task-based detectability in CT image reconstruction by filtered backprojection and penalized likelihood estimation. Med Phys. 2014;41(8):260–78.Google Scholar
  31. 31.
    Hsieh SS, Pelc NJ. Improvements in low contrast detectability with iterative reconstruction and the effect of slice thickness. Medical Imaging 2017: Physics of Medical Imaging. 2017;10132.Google Scholar
  32. 32.
    Gomez-Cardona D, Li K, Hsieh J, Lubner MG, Pickhardt PJ, Chen GH. Can conclusions drawn from phantom-based image noise assessments be generalized to in vivo studies for the nonlinear model-based iterative reconstruction method? Med Phys. 2016;43(2):687–95.PubMedPubMedCentralCrossRefGoogle Scholar
  33. 33.
    Kak AC, Slaney M. Principles of computerized tomographic imaging. New York: IEEE Press; 1988.Google Scholar
  34. 34.
    Hsieh J. Computed tomography principles, design, artifacts, and recent advances. 2nd ed. Hoboken: Wiley; 2009.Google Scholar
  35. 35.
    Szczykutowicz TP, Bour RK, Rubert N, Wendt G, Pozniak M, Ranallo FN. CT protocol management: simplifying the process by using a master protocol concept. J Appl Clin Med Phys. 2015;16(4):228–43.PubMedPubMedCentralCrossRefGoogle Scholar
  36. 36.
    Riederer SJ, Pelc NJ, Chesler DA. The noise power spectrum in computed X-ray tomography. Phys Med Biol. 1978;23(3):446–54.. Epub 1978/05/01CrossRefGoogle Scholar
  37. 37.
    Kijewski MF, Judy PF. The noise power spectrum of Ct images. Phys Med Biol. 1987;32(5):565–75.CrossRefGoogle Scholar
  38. 38.
    Zhang R, Cruz-Bastida JP, Gomez-Cardona D, Hayes JW, Li K, Chen GH. Quantitative accuracy of CT numbers: theoretical analyses and experimental studies. Med Phys. 2018;45(10):4519–28.. Epub 2018/08/14PubMedCrossRefPubMedCentralGoogle Scholar
  39. 39.
    Fessler JA. Hybrid Poisson/polynomial objective functions for tomographic image reconstruction from transmission scans. IEEE Trans Image Process: Publ IEEE Signal Process Soc. 1995;4(10):1439–50.. Epub 1995/01/01CrossRefGoogle Scholar
  40. 40.
    Gomez-Cardona D, Cruz-Bastida JP, Li K, Budde A, Hsieh J, Chen GH. Impact of bowtie filter and object position on the two-dimensional noise power spectrum of a clinical MDCT system. Med Phys. 2016;43(8):4495.. Epub 2016/08/05PubMedPubMedCentralCrossRefGoogle Scholar
  41. 41.
    Whiting BR, editor. Signal statistics in x-ray computed tomography. Medical Imaging 2002. SPIE; 2002.Google Scholar
  42. 42.
    Mandel L. Image fluctuations in Cascade intensifiers. Brit J Appl Phys. 1959;10(5):233–4.CrossRefGoogle Scholar
  43. 43.
    Tapiovaara MJ, Wagner RF. SNR and DQE analysis of broad-Spectrum X-ray-imaging. Phys Med Biol. 1985;30(6):519–29.CrossRefGoogle Scholar
  44. 44.
    Duan X, Wang J, Leng S, Schmidt B, Allmendinger T, Grant K, et al. Electronic noise in CT detectors: impact on image noise and artifacts. AJR Am J Roentgenol. 2013;201(4):W626–32.. Epub 2013/09/26PubMedCrossRefPubMedCentralGoogle Scholar
  45. 45.
    Tward DJ, Siewerdsen JH. Cascaded systems analysis of the 3D noise transfer characteristics of flat-panel cone-beam CT. Med Phys. 2008;35(12):5510–29.. Epub 2009/01/30PubMedPubMedCentralCrossRefGoogle Scholar
  46. 46.
    Sohval AR, Freundlich D, inventors. Plural source computed tomography device with improved resolution 1986.Google Scholar
  47. 47.
    Lonn AH, inventor. Computed tomography system with translatable focal spot 1990.Google Scholar
  48. 48.
    Hsieh J, Gard M, Gravelle S. A reconstruction technique for focal spot wobbling. Proc Soc Photo-Opt Ins. 1992;1652:175–82.Google Scholar
  49. 49.
    Hsieh J, Saragnese EL, Stahre JE, Dorri B, Kaufman J, Senzig RF, inventors. Methods and apparatus for x-ray imaging with focal spot deflection 2008.Google Scholar
  50. 50.
    Kachelriess M, Knaup M, Penssel C, Kalender WA. Flying focal spot (FFS) in cone-beam CT. Ieee T Nucl Sci. 2006;53(3):1238–47.CrossRefGoogle Scholar
  51. 51.
    Cruz-Bastida JP, Gomez-Cardona D, Li K, Sun HY, Hsieh J, Szczykutowicz TP, et al. Hi-Res scan mode in clinical MDCT systems: experimental assessment of spatial resolution performance. Med Phys. 2016;43(5).PubMedPubMedCentralCrossRefGoogle Scholar
  52. 52.
    Cruz-Bastida JP, Gomez-Cardona D, Garrett J, Szczykutowicz T, Chen GH, Li K. Modified ideal observer model (MIOM) for high-contrast and high-spatial resolution CT imaging tasks. Med Phys. 2017;44(9):4496–505.PubMedPubMedCentralCrossRefGoogle Scholar
  53. 53.
    Tward DJ, Siewerdsen JH. Noise aliasing and the 3D NEQ of flat-panel cone-beam CT: effect of 2D/3D apertures and sampling. Med Phys. 2009;36(8):3830–43.PubMedPubMedCentralCrossRefGoogle Scholar
  54. 54.
    Rabbani M, Shaw R, Vanmetter R. Detective quantum efficiency of imaging-systems with amplifying and scattering mechanisms. J Opt Soc Am A. 1987;4(5):895–901.PubMedCrossRefPubMedCentralGoogle Scholar
  55. 55.
    Giger ML, Doi K, Metz CE. Investigation of basic imaging properties in digital radiography .2. Noise wiener Spectrum. Med Phys. 1984;11(6):797–805.PubMedCrossRefPubMedCentralGoogle Scholar
  56. 56.
    Siewerdsen JH, Antonuk LE, ElMohri Y, Yorkston J, Huang W, Boudry JM, et al. Empirical and theoretical investigation of the noise performance of indirect detection, active matrix flat-panel imagers (AMFPIs) for diagnostic radiology. Med Phys. 1997;24(1):71–89.PubMedCrossRefPubMedCentralGoogle Scholar
  57. 57.
    Baek J, Pelc NJ. Effect of detector lag on CT noise power spectra. Med Phys. 2011;38(6):2995–3005.PubMedPubMedCentralCrossRefGoogle Scholar
  58. 58.
    Pineda AR, Tward DJ, Gonzalez A, Siewerdsen JH. Beyond noise power in 3D computed tomography: the local NPS and off-diagonal elements of the Fourier domain covariance matrix. Med Phys. 2012;39(6):3240–52.PubMedPubMedCentralCrossRefGoogle Scholar
  59. 59.
    Yang K, Kwan A, Huang S, Boone J. Noise power properties of a cone-beam CT system for breast Cancer detection. Med Phys. 2008;35(6):2977.. −+CrossRefGoogle Scholar
  60. 60.
    Melnyk R, Boudry J, Liu X, Adamak M. Anti-scatter grid evaluation for wide-cone CT. Medical imaging. Phys Med Imaging. 2014;2014:9033.Google Scholar
  61. 61.
    Hayes JW, Gomez-Cardona D, Zhang R, Li K, Cruz-Bastida JP, Chen GH. Low-dose cone-beam CT via raw counts domain low-signal correction schemes: performance assessment and task-based parameter optimization (part I: assessment of spatial resolution and noise performance). Med Phys. 2018;45(5):1942–56.. Epub 2018/03/14PubMedCrossRefPubMedCentralGoogle Scholar
  62. 62.
    Gomez-Cardona D, Hayes JW, Zhang R, Li K, Cruz-Bastida JP, Chen GH. Low-dose cone-beam CT via raw counts domain low-signal correction schemes: performance assessment and task-based parameter optimization (part II. Task-based parameter optimization). Med Phys. 2018;45(5):1957–69.. Epub 2018/03/14PubMedCrossRefPubMedCentralGoogle Scholar
  63. 63.
    Barrett HH, Gordon SK, Hershel RS. Statistical limitations in transaxial tomography. Comput Biol Med. 1976;6(4):307–23.. Epub 1976/10/01PubMedCrossRefPubMedCentralGoogle Scholar
  64. 64.
    Parker DL. Optimal short scan convolution reconstruction for Fan beam Ct. Med Phys. 1982;9(2):254–7.PubMedCrossRefPubMedCentralGoogle Scholar
  65. 65.
    Baek J, Pelc NJ. The noise power spectrum in CT with direct fan beam reconstruction. Med Phys. 2010;37(5):2074–81.PubMedPubMedCentralCrossRefGoogle Scholar
  66. 66.
    Baek J, Pelc NJ. Local and global 3D noise power spectrum in cone-beam CT system with FDK reconstruction. Med Phys. 2011;38(4):2122–31.PubMedPubMedCentralCrossRefGoogle Scholar
  67. 67.
    Kyprianou LS, Rudin S, Bednarek DR, Hoffmann KR. Generalizing the MTF and DQE to include x-ray scatter and focal spot unsharpness: application to a new microangiographic system. Med Phys. 2005;32(2):613–26.PubMedCrossRefPubMedCentralGoogle Scholar
  68. 68.
    Budde A, Hsieh J, Chen GH. Impact of the distortion of focal spot shape on spatial resolution in MDCT. Med Phys. 2018;45(6):E153.Google Scholar
  69. 69.
    Kalender WA. Computed tomography: fundamentals, system technology, image quality, applications. 3rd ed. Paris: Publicis; 2011.Google Scholar
  70. 70.
    Cunningham IA. Chapter 2. Applied linear-systems theory. In: Beutel J, Kundel HL, Van Metter RL, editors. Handbook of medical imaging volume ! Physics and psychophysics. Bellingham: SPIE Press; 2000. p. 79–160.CrossRefGoogle Scholar
  71. 71.
    Gomez-Cardona D, Budde A, Hayes J, Li K, Chen GH. CT number bias in low dose MDCT with Model Based Iterative Reconstruction (MBIR). Radiological Society of North America 2017 Scientific Assembly and Annual Meeting. Chicago, 2017.Google Scholar
  72. 72.
    Hayes J, Zhang R, Gomez-Cardona D, Cruz Bastida JP, Chen GH. Modified model based iterative reconstruction method to improve CT number accuracy in low-dose CT. Radiological Society of North America 2018 Scientific Assembly and Annual Meeting, Chicago, 2018.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Medical Physics and Department of Radiology, School of Medicine and Public HealthUniversity of Wisconsin-MadisonMadisonUSA

Personalised recommendations