Purpose: The noise power spectrum (NPS) of a CT scanner is commonly measured from a single noise image. However, since CT images are three-dimensional (3D) volume data, they have 3D noise characteristics (3D-NPS). In this study, we clarify the relationship among NPSs measured by various approaches in NPS analysis based on the central slice theorem. Its validity is verified by the NPS measurements using actual 3D noise data.
Methods: We defined the NPSz-projection(fx, fy) that was calculated by the 2D Fourier transform (FT) from the 2D projection of 3D noise data in the patient longitudinal direction, the 3D-NPS(fx, fy, fz) that was calculated by the 3D-FT from the 3D noise data, and the 2D-NPS(fx, fy) that was calculated by the 2D-FT from a single noise image; fx, fy, and fz are spatial frequencies corresponding to the axes of x, y, and z in the reconstructed CT volume, respectively. Based on the central slice theorem, we described that the NPSz-projection(fx, fy=0) was equal to the 3D-NPS(fx, fy=0, fz=0), and the NPS(2D-NPS(fx, fy=0)) was different from the 3D-NPS(fx, fy=0, fz=0). To verify them, we compared the NPSs calculated from actual 3D noise data that were obtained using a cylindrical water phantom.
Results: The 3D-NPS(fx, fy=0, fz=0) matched the NPSz-projection(fx, fy=0) and was different from the 2D-NPS(fx, fy=0).
Conclusion: Based on the central slice theorem, we clarified the relationship among NPSs measured by various approaches in NPS analysis; it is important to understand this and then select an appropriate noise data handling and NPS measurement method.
Keywords: central slice theorem; computed tomography (CT); image noise; noise power spectrum (NPS); projection slice theorem.