Analysis of noise power spectrum for linear and non-linear reconstruction algorithms for CT

With the advent of iterative reconstruction algorithms for CT, there is a significant need to develop analysis tools to characterize the behaviour of such algorithms. The mean and variance are the standard measures to capture the first order and second order moment of CT images. However they fail to capture the complete behaviour of the images when the noise is correlated. The noise in the projection data may be very well approximated to be independant and uncorrelated, however the reconstruction process introduces correlation in the images. Auto-correlation is a good measure to capture the second order moments of an image in the presence of correlated noise. In case of a wide-sense stationary process, the noise power spectrum is the discrete Fourier transform of the covariance matrix. We compare the auto-correlation function and local noise power spectrum of images reconstructed with filtered back-projection (FBP) using a standard kernel, FBP followed by post-processing, and a penalized weighted least square (PWLS) algorithm. A 20 cm uniform water phantom is scanned multiple times in GE Discovery HD750 system and the corresponding 3D auto-correlation function is compared for all three algorithms. The 3D NPS is computed using Welch's periodogram [1] approach and compared for all three algorithms. The PWLS images display auto-correlation function with a longer tail than other algorithms in both axial and coronal planes. The NPS in the axial plane exhibits characteristics of a high-pass filter with all three algorithms sharing the same low-frequency slope. The NPS in the reformatted plane exhibits low-pass filter characteristics with the PWLS algorithm behaving as the best low-pass filter. This may lead to a better detectability in the reformatted planes [2] for images reconstructed with PWLS. The NPS and auto-correlation function is well characterized for three different algorithms and can be utilized for computing detectability using Fourier metrics [2].