A new image reconstruction method to improve noise properties in x-ray differential phase contrast computed tomography

The noise properties of differential phase contrast CT (DPC-CT) demonstrate some peculiar features. It has been both theoretically and experimentally demonstrated that the noise variance of DPC-CT scales with spatial resolution following an inverse first order relationship. This is in stark contrast to absorption CT, where the noise variance scales with spatial resolution following an inverse third power. In addition to the scaling relationship, the noise power spectrum (NPS) of DPC-CT is dominated by low spatial frequencies and demonstrates a singular behavior when approaching zero frequency. This focuses the peak noise power within low spatial frequencies while high-frequency noise is suppressed. This is again in contrast to the absorption CT case where the NPS smoothly transitions to zero at zero frequency. The singular behavior of the DPC-CT NPS visually affects image noise texture and may hinder observer perception. In this paper, a method is proposed to improve the noise properties in DPC-CT and potentially improve observer performance. Specifically, the low frequency component of the filtering kernel used in reconstruction has been regularized to modify the noise power at low spatial frequencies. This results in a high-pass filtering of the image. The high-pass filtered image is combined with the original image to generate the final image. As a result of these two operations, the noise power is shifted to the high spatial frequency direction, improving visual perception, while image reconstruction accuracy is maintained. Experimental phantom results are presented to validate the proposed method.