Nonlinear Model of Image Noise: An Application on Computed Tomography including Beam Hardening and Image Processing Algorithms


This paper proposes a more inclusive statistical model for predicting image noise in Computed Tomography (CT), associated with scanning factors, considering the effect of beam hardening and image processing filters. It is based on power functions where the levels of the parameters will determine the rate of noise variation with respect to a given scanning factor. It includes the influence of tube potential, tube current, slice thickness, Field of View (FOV), reconstruction methods and post-processing filters. To validate the model, tomographic measurements were made by using a PMMA phantom that simulates paediatric head and adult abdomen, a PET bottle was used to simulate the head of the new-born. The influence of ROI (Region Of Interest) size over nonlinear model parameters was analysed, and high variations of powers of attenuation and FOV were found depending on ROI size. A nonlinear robust regression method was used. The validation was performed graphically by weighted residual analysis. A nonlinear noise model was obtained with an adjusted coefficient of determination for ROI sizes between 10% and 70% of the phantom diameter or FOV. The model confirms the significance of the tube current, slice thickness and beam hardening effect on image. The process of estimation of the parameters of the model by Nonlinear Robust Regression turned out to be optimal.

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Miller-Clemente, R. , Diaz, M. , Matamoros, L. and Edyvean, S. (2014) Nonlinear Model of Image Noise: An Application on Computed Tomography including Beam Hardening and Image Processing Algorithms. Applied Mathematics, 5, 1240-1251. doi: 10.4236/am.2014.58116.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Brooks, R.A. and Chiro, G.D. (1976) Statistical Limitations in X-Ray Reconstructive Tomography. Medical Physics, 3, 237-240.
[2] KachelrieB, M. and Kalender, W.A. (2005) Presampling, Algorithm Factors, and Noise: Considerations for CT in Particular and for Medical Imaging in General. Medical Physics, 32, 1321-1334.
[3] Ledenius, K., Gustavsson, M., Johansson, S., StAlhammar, F., Soderberg, J., Wiklund, L.M. and Klang, A.T. (2005) A Method of Predicting the Image Noise in Paediatric Multi-Slice Computed Tomography Images. Radiation Protection Dosimetry, 114, 313-316.
[4] Starck, G., Lonn, L., Cederblad, A., Forsell-Aronsson, E., Sjostrom, L. and Alpsten, M. (2002) A Method to Obtain the Same Levels of CT Image Noise for Patients of Various Sizes, to Minimize Radiation Dose. The British Journal of Radiology, 75, 140-150.
[5] Kalender, W.A. (2005) Computed Tomography. Publicis Corporate Publishing, Erlangen.
[6] Chabior, M., Donath, T., David, C., Bunk, O., Schusterb, M., Schroer, C. and Pfeiffer, F. (2011) Beam Hardening Effects in Grating-Based X-Ray Phase-Contrast Imaging. Medical Physics, 38, 1189-1195.
[7] Alles, J. and Mudde, R.F. (2007) Beam Hardening: Analytical Considerations of the Effective Attenuation Coefficient of X-Ray Tomography. Medical Physics, 34, 2882-2889.
[8] Boone, J.M. and Chavez, A.E. (1996) Comparison of X-Ray Cross Sections for Diagnostic and Therapeutic Medical Physics. Medical Physics, 23, 1997-2005.
[9] Nowotny, R. and Hofer, A. (1985) Ein program fur die berechnung von diagnostischen Rontgenspektren. Fortschr Rontgenstr, 142, 685-689.
[10] Kutner, M.H., Nachtsheim, C.J., Neter, J. and Li, W. (2005) Applied Linear Statistical Models. McGraw-Hill, Singapore City.
[11] SHIMADZU (2004) Instruction Manual: SHIMADZU X-Ray Computerized Tomography System SCT-7800 TC Series. SHIMADZU, Kyoto.
[12] Graybill, F.A. and Iyer, H.K. (1994) Regression Analysis: Concepts and Applications. Belmont, California.
[13] Nickoloff, E.L., Dutta, A.K. and Zheng, F.L. (2003) Influence of Phantom Diameter, kVp and Scan Mode upon Computed Tomography Dose Index. Medical Physics, 30, 395-402.
[14] Miller-Clemente, R.A., Pérez-Díaz, M., Lores Guevara, M., Ortega Rodríguez, O., Nepite Haber, R., Grinán Hernández, O. and Guillama Llossas, A. (2013) Optimización mediante control automático de exposición para estudios de fosa posterior en TC pediátrica. Imagen Diagnóstica, 4, in Press.

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