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.

翻译：从相干X射线测量中恢复高分辨率结构与成分信息涉及求解耦合、非线性且不适定的反问题。叠层成像从重叠的衍射图案中重建复透射函数，而X射线荧光则以较低空间分辨率提供定量的元素特异性对比度。我们构建了一个联合变分框架，将这两种模态整合为一个具有共享空间变量的非线性最小二乘问题。该框架强制结构与成分估计之间的跨模态一致性，改善了问题条件并促进了稳定收敛。所得优化在统一的反演模型中将互补的对比机制（即叠层成像的相位与吸收、荧光的元素组成）耦合起来。基于模拟数据的数值实验表明，与单独反演相比，联合重建实现了更快的收敛速度、更清晰且更定量的重建结果以及更低的相对误差。所提出的方法展示了多模态变分框架如何提升计算X射线成像的稳定性、分辨率与可解释性。