Criteria for selecting the Paganin-filter reconstruction parameter in X-ray phase-contrast tomography

The Paganin filter, widely employed in propagation-based phase-contrast X-ray computed tomography with synchrotron light, attenuates phase effects and suppresses high-frequency noise under the assumption that samples have a constant β/δ ratio (these constants define the material's complex refractive index n = 1 - δ + iβ). While effective in many scenarios, real samples often violate this strong assumption, and the choice of the filter's free reconstruction parameter is typically made empirically, potentially leading to suboptimal image quality. This work introduces a quantitative, noise-aware criterion for determining a near-optimal filter parameter, thereby removing the need for subjective tuning. We propose two methods for this task. The first method is based on analysis of the noise power spectrum in radial frequency bands, adopting the same partitioning framework as Fourier ring correlation (FRC). By monitoring high-frequency behavior, the proposed approach identifies the trade-off point where resolution enhancement is balanced against noise amplification. This criterion enforces a theoretical lower bound on the FRC computed between two independently split Paganin-filtered projections, where each projection corresponds to a single recorded detector frame, while ensuring effective suppression of high-frequency noise. The second method analyzes the variation of the reconstructed images as a function of the Paganin-filter parameter, identifying the inflection point that represents the balance between noise suppression and image smoothing. Both methods result in an automated parameter selection approach for phase-contrast tomography data analysis that employs the Paganin filter.