Noise characterization of computed tomography using the covariance matrix

In order to compare different imaging systems, it is necessary to obtain detailed information about the system noise, its deterministic properties and task specific signal-to-noise ratio (SNR). The current standard method for characterizing noise in CT scanners is based on the pixel standard deviation of the image of a water-equivalent, uniform phantom. The Fourier-based noise power spectrum (NPS) improves on the limitations of the pixel standard deviation by accounting for noise correlations. However, it has been shown that the Fourier-methods used to describe the system performance result in systematic errors as they make some limiting assumptions such as shift invariance and wide sense stationarity, which are not satisfied by real CT systems. For a more general characterization of the imaging system noise, a covariance matrix eigenanalysis can be performed. In this paper we present the experimental methodology for the evaluation of the noise of computed tomography systems. We used a bench-top flat-panel-based cone-beam CT scanner and a cylindrical water-filled PMMA phantom. For the 3-diinensional reconstructed volume, we calculated the covariance matrix, its eigenvectors and eigenvalues for the xy-plane as well as for the yz-plane, and compared the results with the NPS. Furthermore, we analyzed the location-specific noise in the images. The evaluation of the noise is a first step toward determining the task-specific SNR.