A Joint Variational Framework for Multimodal X-ray Ptychography and Fluorescence Reconstruction

TL;DR

This work develops a joint variational framework to fuse X-ray ptychography and XRF by coupling their data fidelities through a physics-guided link, yielding a single nonlinear least-squares objective with shared spatial variables. The approach leverages GradNorm to balance contributions from the two modalities and analyzes the Jacobian and Hessian to show enhanced conditioning and richer optimization directions. Numerical experiments on synthetic data demonstrate faster convergence, sharper reconstructions, and greater robustness to noise and varying overlap, including multi-element maps. The proposed multimodal formulation improves quantitative accuracy and stability in computational X-ray imaging, with potential to exceed nominal probe-limited resolution in fluorescence via joint deconvolution.

Abstract

Recovering high-resolution structural and compositional information from coherent X-ray measurements involves solving coupled, nonlinear, and ill-posed inverse problems. Ptychography reconstructs a complex transmission function from overlapping diffraction patterns, while X-ray fluorescence provides quantitative, element-specific contrast at lower spatial resolution. We formulate a joint variational framework that integrates these two modalities into a single nonlinear least-squares problem with shared spatial variables. This formulation enforces cross-modal consistency between structural and compositional estimates, improving conditioning and promoting stable convergence. The resulting optimization couples complementary contrast mechanisms (i.e., phase and absorption from ptychography, elemental composition from fluorescence) within a unified inverse model. Numerical experiments on simulated data demonstrate that the joint reconstruction achieves faster convergence, sharper and more quantitative reconstructions, and lower relative error compared with separate inversions. The proposed approach illustrates how multimodal variational formulations can enhance stability, resolution, and interpretability in computational X-ray imaging.

Figures (21)

• Figure 1: An illustration of a joint ptychographic and fluorescence experiment.
• Figure 1: Normalized eigenvalue distribution comparison in reconstruction.
• Figure 1: Magnitude (left) and phase (right) of the simulated probe matrix used in numerical experiments.
• Figure 2: True point gradient norm perturbation log-scale plot with illustration.
• Figure 2: Reconstruction results for ptychography only, fluorescence only and the joint method on a synthetic object of size $n=154$ with probe size $m=64$, using $\text{Noise Level} = 3\%$ and overlap ratio $0.83$. The joint method achieves more accurate reconstructions.