[论文解读] Fast Eikonal Phase Retrieval for High-Throughput Beamlines

Alessandro Mirone, Theresa Urban+4 more|arXiv (Cornell University)|Jan 30, 2026

Advanced X-ray Imaging Techniques被引用 0

一句话总结

本文提出一个快速的二阶 Eikonal 相位回退（EPR）框架，结合局部 L^2 闭包和非局部多像素光线映射求解器，在高吞吐 PPC-μCT 下实现 >100× 的加速，同时保持精度并支持多色数据。

ABSTRACT

We introduce a fast Eikonal Phase Retrieval (EPR) formulation that accelerates eikonal phase retrieval by more than two orders of magnitude while retaining controlled accuracy. The method is derived from a second-order asymptotic expansion in the propagation distance $L$ and complemented by the leading Wentzel--Kramers--Brillouin (WKB) wave-optics correction, yielding an efficient iterative correction scheme preconditioned by FFT-diagonal, energy-dependent inverse operators (Paganin-type filters). To ensure robustness across practical experimental regimes, we combine two complementary solvers: (i) a local $O(L^2)$ closure that is accurate when eikonal shifts remain sub-pixel, and (ii) a non-local formulation for multi-pixel shifts, in which intensity is propagated through an explicit eikonal ray mapping using a mass-conserving bilinear redisribution on the detector grid, and detector residuals are transferred back to the object grid by the corresponding adjoint (transpose), implemented as bilinear interpolation, before applying an approximate FFT-diagonal preconditioner to accelerate convergence. The same framework supports polychromatic data through a compact spectral discretisation, allowing energy-dependent transport and inversion while keeping the iteration GPU/FFT efficient. Overall, this unified approach enables accurate and computationally efficient phase retrieval across propagation conditions relevant to high-throughput PPC-$μ$CT experiments.

研究动机与目标

• Motivate propagation-based phase-contrast micro-tomography (PPC-μCT) for high-throughput beamlines and address nonlinear artefacts at long propagation distances.
• Develop a fast EPR formulation that retains the full O(L^2) WKB-based forward model with a leading WKB1 correction.
• Ensure robustness across sub-pixel and multi-pixel shift regimes with a complementary local and non-local solver.
• Incorporate polychromatic (spectral) data handling to improve quantitative accuracy.
• Demonstrate substantial computational acceleration relative to prior EPR implementations while preserving reconstruction quality.

提出的方法

• Retain the complete O(L^2) content of a WKB (saddle-point) expansion of the Fresnel propagator (WKB0 transport plus leading WKB1 correction).
• Use FFT-diagonal preconditioning (Paganin-type filters) to accelerate convergence in an iterative scheme.
• Introduce a non-local forward model that explicitly transports intensity via a WKB0 ray mapping and uses mass-conserving bilinear redistribution on the detector grid; back-project residuals via the explicit adjoint (transpose).
• Operate in a polychromatic framework by discretising the spectrum into a small number of effective spectral lines and summing their contributions.
• Enforce a single-thickness constraint across spectral lines via a low-dimensional manifold projection to stabilize the multi-spectral inversion.

Figure 1: Full reconstructed slice of the sheep-head HiP-CT dataset (same specimen and acquisition context as in the original EPR paper). The yellow rectangle marks the region of interest (ROI) used for the detailed comparisons in Figs. 2 – 5 . Among the multiple zoomed regions discussed in the orig

实验结果

研究问题

• RQ1 Can a second-order near-field model (WKB0+WKB1) combined with FFT-based preconditioning reduce EPR computation time by orders of magnitude without sacrificing accuracy?
• RQ2 How can one robustly handle regimes where eikonal shifts exceed a pixel (multi-pixel transport) while maintaining convergence and stability?
• RQ3 Does incorporating polychromatic data via a compact spectral discretisation improve phase retrieval accuracy and artifact suppression in high-throughput PPC-μCT?
• RQ4 What are the comparative performance and robustness trade-offs between local (sub-pixel) and non-local (multi-pixel) solvers in realistic HiP-CT-like datasets?
• RQ5 How does the accelerated EPR perform on challenging, high-gradient specimens (e.g., bone-soft tissue interfaces) under long-propagation conditions?

主要发现

Configuration	Ns	Iter.	Time
L1 mono (Paganin) on CPU	1	1	45 s
Local L2 mono on GPU	1	1	1.1 min
Local L2 mono on GPU	1	2	1.23 min
Local L2 poly on GPU	5	1	1.47 min
Non-local poly on GPU (oversampling 2)	5	1	2 min
Original EPR implementation	5	many	870 min

• The L^2 second-order (WKB0+WKB1) forward model substantially reduces nonlinear streak artefacts compared to L^1 models, improving soft-tissue contrast in challenging regions.
• Polychromatic modelling provides consistent improvements over monochromatic assumptions, with further gains from the L^2 forward physics.
• The non-local solver remains robust when local sub-pixel assumptions fail (shifts >1 pixel), whereas the local solver can diverge in strong-shift regimes.
• The L^2 poly (polychromatic) approach converges rapidly, with most gains seen after the first L^2 update (often within one iteration).
• Compared with the original EPR, the new implementation reduces phase-retrieval wall time per volume by about 2.8 orders of magnitude on the same GPU resources (≈580× faster).
• A five-spectral-line, single-volume dataset processed with a GPU can achieve near- to mid-minute runtimes per 8000 radiographs, enabling high-throughput workflows.

Figure 2: ROI comparison (brain region) for the four forward models. Top row: monochromatic models; bottom row: polychromatic models. Left column: first-order model $L^{1}$ ; right column: second-order model $L^{2}$ . (Here $L^{1}$ mono is equivalent to the Paganin single-distance forward model in t