Propagation-Based X-Ray Phase Contrast Computed Tomography with the Multislice Approximation and Automatic Differentiation
Abstract
Purpose
Propagation-based X-ray phase contrast computed tomography (PB-XPCT) reconstructs the complex index of refraction whose real part, responsible for the phase shifting of x-rays, is known to differ more among soft tissues than the imaginary part, responsible for the usual attenuation of x-rays. Reconstruction for PB-XPCT typically relies on the projection approximation (PA) model that is only valid for relatively thin samples. Instead, we investigate gains in image quality using a multislice (MS) model made computationally feasible with automatic differentiation (AD).
Methods
We implemented both models in Chromatix, which includes AD natively. We then simulated monochromatic XPC-CT data at 10 keV using MS for a computational phantom consisting of bone inserts in a tissue cylinder under low and high Poisson noise and at three voxel sizes (0.5 µm, 0.25 µm, and 0.1 µm with phantom thicknesses 32 µm, 16 µm, and 6.4 µm, respectively). We implemented iterative reconstructions for both models in Optax, with total variation regularization terms for both the real component of the refractive index (i.e., phase images) and the imaginary component (i.e., attenuation images). The regularization weights were tuned via a parameter search. We assessed the reconstructed phase and attenuation images using total root mean square error (RMSE), material accuracy, and signal to noise ratios (SNR).
Results
At all voxel sizes, MS gave phase images with lower RMSEs (e.g. 1.69x10-8 and 3.31x10-8, respectively, with 0.1 µm voxels at low noise), closer agreement to ground truth, and better SNRs relative to PA at both noise levels. Geometrically accurate attenuation reconstructions were only obtainable at low noise, where MS likewise produced images with superior RMSEs, material agreements, and SNRs.
Conclusion
Our findings suggest that using MS in iterative reconstruction of PB-XPCI data results in a measurable improvement in image quality against PA in the regime of voxel sizes explored.