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

Abstract

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.