Deriving the modulation transfer function of CT from extremely noisy edge profiles

The point spread function (PSF) method is currently the one predominantly used to determine the modulation transfer function (MTF) of an X-ray CT system. However, the image examined with the PSF method must have a very high contrast-to-noise ratio (CNR); it must also be reconstructed with a fine pixel pitch using a zooming reconstruction. Therefore, the PSF method is often inappropriate for describing the MTF of clinical operating conditions when image linearity is not guaranteed. The edge spread function (ESF) method requires no zooming reconstruction, but its susceptibility to image noise is no better than that of the PSF method. We describe a technique for rendering the ESF method robust to image noise. We smooth out the noisy ESF through multiple stages of filtering. Invariably, the line spread function (LSF) obtained from the smoothed ESF is blurred, and the MTF obtained from the LSF is incorrect. However, because the filtering that has been applied is known, much of the LSF blurring can be corrected. An estimate of the true LSF is obtainable from the blurred LSF, assuming that the true LSF is not very different from either a Gaussian or a composite of multiple Gaussians. For an image reconstructed with a kernel for soft-tissue imaging, the MTF obtained by our method is sufficiently consistent with the theoretical MTF, even when the CNR is as low as 2.