Effect of noise in CT image reconstruction using QR-Decomposition algorithm

The QR-Decomposition algorithm for CT 3D image reconstruction uses a linear system of equations to model the CT system response. Linear systems have a condition number that can be used to estimate the image noise. In this work the number of projections and the number of pixels in the detector have been studied to characterize the CT and the linear system of equations. The condition number of the system is estimated for the previous parameters used to generate the CT model with the aim of characterizing how these parameters affect the condition number and therefore bound the image noise level. It is shown that the condition number mainly depends on the size of pixels of the detector rather than the number of projections and this algorithm can be applied to low dose CT 3D image reconstruction without compromising image quality.