Method to calculate frequency characteristics of reconstruction filter kernel in X-ray computed tomography

A computed tomography (CT) image is generally reconstructed by a filtered back projection (FBP) algorithm. In an FBP algorithm, the image quality primarily depends on a reconstruction filter kernel. Although the details of the filter kernel are not disclosed to users, the frequency response of the filter kernel can theoretically be calculated using the relational formula of the filter kernel and the modulation transfer function (MTF) of the reconstruction algorithm (MTF_A). In this study, we proposed a method to determine the frequency response of a filter kernel and verify its validity. Two clinical CT scanners were used to derive the filter kernel. The MTF was obtained and subsequently separated to the MTF of the scanner system and MTF_A. Using the relational formula of the filter kernel and MTF_A, we calculated the frequency response of the filter kernel. To verify the calculated result, we measured the noise power spectrum (NPS). Additionally, the filter kernel was calculated using the relational formula of the filter kernel and NPS. In both CT scanners, the filter kernels calculated by the two methods showed good agreement, and we confirmed the validity of the results and the effectiveness of the proposed method. Furthermore, the inherent image quality performance of the CT scanner could be clarified by the reconstruction filter kernel.