A Joint Variational Framework for Multimodal X-ray Ptychography and Fluorescence Reconstruction
This work addresses the challenge of recovering high-resolution structural and compositional information from X-ray measurements for computational imaging researchers, but the results are demonstrated only on simulated data, making it an incremental contribution.
The paper proposes a joint variational framework for multimodal X-ray ptychography and fluorescence reconstruction, integrating structural and compositional data into a single optimization problem. On simulated data, the joint reconstruction achieves faster convergence, sharper quantitative reconstructions, and lower relative error compared to separate inversions.
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.