[Method for Measuring Noise Power Spectrum Depending on X-ray Tube Angle in Spiral Orbit of Helical CT Scan].

PURPOSE: The noise power spectrum (NPS) in computed tomography (CT) images potentially varies with the X-ray tube angle in a spiral orbit of the helical scan. The purpose of this study was to propose a method for measuring the NPS for each angle of the X-ray tube. METHODS: Images of the water phantom were acquired using a helical scan. As a conventional method, we measured the two-dimensional (2D) NPS from each image and averaged them; the obtained 2D-NPS was referred to as NPSconventional. In the proposed method, we made the X-ray tube angle θ (0°≤θ<360°) to correspond to the image according to each slice position of the images that located within the travel distance of the CT scan table per 360° rotation of the X-ray tube. We obtained the 2D-NPS from each image and assigned the θ (0°, 30°, 60°, 90°, 120°, 150°, 180°); the obtained 2D-NPS was referred to as NPSsθ. The NPSsθ was compared to the NPSconventional. Also, we investigated the dependency of the NPSsθ on the θ. RESULTS: The NPSconventional was found to be isotropic, and in contrast, the NPSsθ was anisotropic. The NPSsθ showed a continuously rotational change while increasing the θ. There was an excellent correlation (R2>0.999) between the rotation angle of NPSθ and the θ. CONCLUSION: The proposed method was demonstrated to be effective for evaluating anisotropic noise characteristics depending on the X-ray tube angle.

Method for measuring noise-power spectrum independent of the effect of extracting the region of interest from a noise image.

This study aimed to evaluate the impact of region of interest (ROI) size on noise-power spectrum (NPS) measurement in computed tomography (CT) images and to propose a novel method for measuring NPS independent of ROI size. The NPS was measured using the conventional method with an ROI of size P × P pixels in a uniform region in the CT image; the NPS is referred to as NPSR=P. NPSsR=256, 128, 64, 32, 16, and 8 were obtained and compared to assess their dependency on ROI size. In the proposed method, the true NPS was numerically modeled as an NPSmodel, with adjustable parameters, and a noise image with the property of the NPSmodel was generated. From the generated noise image, the NPS was measured using the conventional method with a P × P pixel ROI size; the obtained NPS was referred to as NPS'R=P. The adjustable parameters of the NPSmodel were optimized such that NPS'R=P was most similar to NPSR=P. When NPS'R=P was almost equivalent to NPSR=P, the NPSmodel was considered the true NPS. NPSsR=256, 128, 64, 32, 16, and 8 obtained using the conventional method were dependent on the ROI size. Conversely, the NPSs (optimized NPSsmodel) measured using the proposed method were not dependent on the ROI size, even when a much smaller ROI (P = 16 or 8) was used. The proposed method for NPS measurement was confirmed to be precise, independent of the ROI size, and useful for measuring local NPSs using a small ROI.

[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(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.