Transport-of-Intensity Equation for Real-Time Tomographic Experiments: Projection or Slices? - Eduardo X. Miqueles; Paola C. Ferraz; Goran Lovric; David M. Paganin (IEEE Access, 2025)
In this manuscript, we present a computational imaging discussion on the classical Paganin approach for recovering the phase of X-ray tomographic measurements using the Transport-of-Intensity Equation (TIE) with a single-material parameter. In practical experiments, this parameter often carries significant uncertainty, leading tomographic users to iteratively test various values until a reconstruction provides useful information. From a computational perspective, this trial-and-error process affects user experience, as it is both time-consuming and resource-intensive. We compare the classical formulation of the problem in the projection domain (also referred to as the frame domain) with an alternative filtering strategy in the sinogram domain (also referred to as the slice domain). Additionally, we propose bounds to quantify the differences between these approaches. Processing directly in the slice domain is significantly faster, as the phase retrieval is integrated with the reconstruction process, effectively combining two steps into one. This integration enhances the user experience in tomographic beamline settings.