Precise phase retrieval for propagation-based images using discrete mathematics

TL;DR

This paper develops a discrete mathematics-based approach to phase retrieval in propagation-based X-ray imaging, significantly improving spatial resolution especially with detectors that have minimal PSF effects.

Contribution

It rederives phase retrieval algorithms using discrete mathematics, enhancing spatial resolution in CT imaging for single- and multi-material objects.

Findings

Up to 17% resolution improvement with single pixel PSF detectors.

Discrete derivation offers limited gains when high-frequency components are suppressed.

Validated through experimental CT reconstructions of phantoms and tissue.

Abstract

The ill-posed problem of phase retrieval in optics, using one or more intensity measurements, has a multitude of applications using electromagnetic or matter waves. Many phase retrieval algorithms are computed on pixel arrays using discrete Fourier transforms due to their high computational efficiency. However, the mathematics underpinning these algorithms is typically formulated using continuous mathematics, which can result in a loss in spatial resolution in the reconstructed images. Herein we investigate how phase retrieval algorithms for propagation-based phase-contrast X-ray imaging can be rederived using discrete mathematics and result in more precise retrieval for single- and multi-material objects and for spectral image decomposition. We validate this theory through experimental measurements of spatial resolution using computed tomography (CT) reconstructions of plastic phantoms and biological tissue, using detectors with a range of imaging system point spread functions (PSFs). We demonstrate that if the PSF substantially suppresses high spatial frequencies, the potential improvement from utilising the discrete derivation is limited. However, with detectors characterised by a single pixel PSF (e.g. direct, photon-counting X-ray detectors), a significant improvement in spatial resolution can be obtained, demonstrated here at up to 17%.