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.
Cite this paper
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
, 1240-1251. doi: 10.4236/am.2014.58116
 Brooks, R.A. and Chiro, G.D. (1976) Statistical Limitations in X-Ray Reconstructive Tomography. Medical Physics, 3, 237-240. http://dx.doi.org/10.1118/1.594240
 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.
 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.
 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.
 Kalender, W.A. (2005) Computed Tomography. Publicis Corporate Publishing, Erlangen.
 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.http://dx.doi.org/10.1118/1.3553408
 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. http://dx.doi.org/10.1118/1.2742501
 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. http://dx.doi.org/10.1118/1.597899
 Nowotny, R. and Hofer, A. (1985) Ein program fur die berechnung von diagnostischen Rontgenspektren. Fortschr Rontgenstr, 142, 685-689. http://dx.doi.org/10.1055/s-2008-1052738
 Kutner, M.H., Nachtsheim, C.J., Neter, J. and Li, W. (2005) Applied Linear Statistical Models. McGraw-Hill, Singapore City.
 SHIMADZU (2004) Instruction Manual: SHIMADZU X-Ray Computerized Tomography System SCT-7800 TC Series. SHIMADZU, Kyoto.
 Graybill, F.A. and Iyer, H.K. (1994) Regression Analysis: Concepts and Applications. Belmont, California.
 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. http://dx.doi.org/10.1118/1.1543149
 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.