Nihon Hoshasen Gijutsu Gakkai zasshi · 2022
[A Study of Longitudinal NPS Measurement in CT Images Based on the Central Cross-section Theorem].
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Narita Akihiro, Ohkubo Masaki, Ohsugi Yuki, Sakai Kenichi, Fukaya Takahiro, Noto Yoshiyuki
Аннотация
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(fx, fy, fz) that was calculated by 3D Fourier transform (FT) from 3D noise data (3D-Noise(x, y, z), x-y scan plane). Here, fx, fy and fz 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 fz-directional NPS calculated from the 3D-Noise(x=0, y=0, z) is equal to the profile obtained by projecting 3D-NPS(fx, fy, fz) in fx- and fy-directions. (2) The fz-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 fy=0 in the data obtained by projecting 3D-NPS(fx, fy, fz) in the fx-direction. (3) The fz-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(fx=0, fy=0, fz). 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 fz-directional NPS matched the profile obtained from the 3D-NPS(fx, fy, fz).
CONCLUSION: Based on the central slice theorem, we clarified the relationships between fz-directional NPSs and 3D-NPS. We should understand them and then consider which method should be used for fz-directional NPS measurement.
METHODS: We defined the 3D-NPS(fx, fy, fz) that was calculated by 3D Fourier transform (FT) from 3D noise data (3D-Noise(x, y, z), x-y scan plane). Here, fx, fy and fz 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 fz-directional NPS calculated from the 3D-Noise(x=0, y=0, z) is equal to the profile obtained by projecting 3D-NPS(fx, fy, fz) in fx- and fy-directions. (2) The fz-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 fy=0 in the data obtained by projecting 3D-NPS(fx, fy, fz) in the fx-direction. (3) The fz-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(fx=0, fy=0, fz). 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 fz-directional NPS matched the profile obtained from the 3D-NPS(fx, fy, fz).
CONCLUSION: Based on the central slice theorem, we clarified the relationships between fz-directional NPSs and 3D-NPS. We should understand them and then consider which method should be used for fz-directional NPS measurement.