[A Study of Longitudinal NPS Measurement in CT Images Based on the Central Cross-section Theorem]

Purpose: Various approaches in noise power spectrum (NPS) analysis are currently used for measuring a patient's longitudinal (z-direction) NPS from three-dimensional (3D) CT volume data. The purpose of this study was to clarify the relationship between those NPSs and 3D-NPS based on the central slice theorem.

Methods: We defined the 3D-NPS(f_x, f_y, f_z) that was calculated by 3D Fourier transform (FT) from 3D noise data (3D-Noise(x, y, z), x-y scan plane). Here, f_x, f_y and f_z are spatial frequencies corresponding to the axes of x, y and z, respectively. Based on the central slice theorem, we described three relationships as follows. (1) The f_z-directional NPS calculated from the 3D-Noise(x=0, y=0, z) is equal to the profile obtained by projecting 3D-NPS(f_x, f_y, f_z) in f_x- and f_y-directions. (2) The f_z-directional NPS calculated from the profile obtained by projecting 3D-Noise(x=0, y, z) in the y-direction is equal to the profile at f_y=0 in the data obtained by projecting 3D-NPS(f_x, f_y, f_z) in the f_x-direction. (3) The f_z-directional NPS calculated from the profile obtained by projecting 3D-Noise(x, y, z) in x and y-directions is equal to the profile of 3D-NPS(f_x=0, f_y=0, f_z). To verify them, we compared the NPSs measured from actual 3D noise data that were obtained using a cylindrical water phantom.

Results: In each relationship (1)-(3), the f_z-directional NPS matched the profile obtained from the 3D-NPS(f_x, f_y, f_z).

Conclusion: Based on the central slice theorem, we clarified the relationships between f_z-directional NPSs and 3D-NPS. We should understand them and then consider which method should be used for f_z-directional NPS measurement.