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

TL;DR

This paper introduces a joint variational framework that combines ptychography and fluorescence X-ray imaging to improve reconstruction quality, stability, and convergence in multimodal X-ray inverse problems.

Contribution

It formulates a unified nonlinear least-squares model integrating structural and compositional data, enforcing cross-modal consistency for enhanced imaging results.

Findings

Joint reconstruction achieves faster convergence.

Results show sharper, more quantitative images.

Lower relative error compared to separate methods.

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.