Several experimental studies of the noise power spectrum (NPS) of cone-beam CT have been performed, but less attention has been paid to the analytical derivation of the 3D NPS. It is well known that noise in cone beam CT is nonstationary. When the image is reconstructed by using the FDK algorithm, different back-projection and cosine weightings are used for different reconstruction regions. In addition, the ray density and cone angle are also spatially dependent. As a result, a cone beam system has non-stationary noise. In order to characterize the noise behavior, we first construct the 3D NPS in a local reconstruction volume. Because cone beam rays passing through a small volume can be approximated as parallel rays, the 3D NPS of a small volume can be constructed by considering all effects. The 3D NPS of a large volume (which describes the average noise behavior but may not be valid throughout the volume) was generated by summing 3D NPS of small sub-volumes. The method was validated with computer simulations with uniform noise in the projection. 3D noise spectra of 3cm, 6cm, and 10 cm thick volumes were generated, and the radial NPS at different kz planes were compared with those of the analytically constructed 3D NPS. The results showed excellent matching for all cases. With the proposed method, non-stationary noise behavior of any local volume can be analyzed. The non-stationary noise behavior also causes a high-frequency roll-off in the NPS of a large volume, and as the volume size increases, the roll-off frequency decreases because the larger volume has more heterogeneous noise behavior.

Date Published: 12 March 2009
PDF: 7 pages
Proc. SPIE 7258, Medical Imaging 2009: Physics of Medical Imaging, 725805 (12 March 2009); doi: 10.1117/12.813832

Published in SPIE Proceedings Vol. 7258:
Medical Imaging 2009: Physics of Medical Imaging
Ehsan Samei; Jiang Hsieh, Editor(s)