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.

I. Introduction

The QR-Decomposition algorithm is classified as a model-based (MB) method [1]. MB reconstruction algorithms allow a detailed mathematical description of the physical processes involved in tomographic systems [2], [3]. This advantage can reduce image artifacts and noise and leads toward dose reduction in CT. Model-based iterative reconstruction (MBIR) method is often considered as a general designation for all MB methods [4]. MBIR algorithms arise a large size optimization problem as well as a careful choice of an optimization function along with an iterative search of the solution in which each step involves two matrix vector products. The QR-Decomposition algorithm takes advantage of the benefits of the MB approach, but only requires a matrix vector product and backward substitution for the image reconstruction. It could be broadly labeled as a model-based direct reconstruction (MBDiR). QR decomposition process can be computed a priori and it is only necessary to compute them once.