Analysis of image noise in 3D cone-beam CT: Spatial and fourier domain approaches under conditions of varying stationarity

The statistical properties of medical images are central in characterizing the performance of imaging systems. The noise in cone-beam CT (CBCT) is often characterized using Fourier-based metrics, such as the 3D noise-power spectrum (NPS). Under a stationarity assumption, the NPS provides a complete representation of the covariance of the images, since the covariance matrix of the Fourier transform of the image is diagonal. In practice, such assumptions are obeyed to varying degrees. The objective of this work is to investigate the degree to which such assumptions apply in CBCT and to experimentally characterize the NPS and off-diagonal elements under a range of experimental conditions. A benchtop CBCT system was used to acquire 3D image reconstructions of various objects (air and a water cylinder) across a range of experimental conditions that could affect stationarity (bowtie filter and dose). We test the stationarity assumption under such varying experimental conditions using both spatial and frequency domain measures of stationarity. The results indicate that experimental conditions affect the degree of stationarity and that under some imaging conditions, local descriptions of the noise need to be developed to appropriately describe CBCT images. The off-diagonal elements of the DFT covariance matrix may not always be ignored.