The noise characteristics of x-ray differential phase contrast computed tomography (DPC-CT) were investigated. Both theoretical derivation and experimental results demonstrated that the dependence of noise variance on spatial resolution in DPC-CT follows an inverse linear law. This behavior distinguishes DPC-CT from conventional absorption based x-ray CT, where the noise variance varies inversely with the cube of the spatial resolution. This anomalous noise behavior in DPC-CT is due to the Hilbert filtering kernel used in the CT reconstruction algorithm, which equally weights all spatial frequency content. Additionally, we demonstrate that the noise power of DPC-CT is scaled by the inverse of spatial frequency and is highly concentrated at the low spatial frequencies, whereas conventional absorption CT increases in power at the high spatial frequencies.
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