Noise Analysis in Computed Tomography (CT) Image Reconstruction using QR-Decomposition Algorithm

In this paper, the noise of 3D computed tomography (CT) image reconstruction using QR-Decomposition is analyzed. There are several types of image noise that can interfere with the interpretation of an image. Here, the noise introduced by the reconstruction process is studied. In this analysis, condition numbers are calculated with different CT model parameters, three dimensional (3D) CT image reconstruction with simulated and real data are performed, image noise analysis is performed through various image quality parameters and the condition number of the linear system is related with the image quality parameters. Results show the condition number's dependence on the CT model. Image reconstructions with simulated data show errors significantly below the condition number theoretical bound and image reconstructions with real data show that quality improvements depend strongly on the condition number. This allows a reduction on the number of projections without compromising image quality and places this reconstruction method as a strong candidate for low-dose 3D CT imaging reconstruction.