Physics-Informed Neural Link Function for Multimodal X-ray Ptychography and Fluorescence Reconstruction Restricted; Files Only

Abstract

Recovering high-resolution structural and compositional information from coherent X-ray measurements requires solving coupled, nonlinear, and ill-posed inverse problems. In this setting, ptychography reconstructs a complex transmission function from overlapping diffraction patterns, while X-ray fluorescence provides quantitative, element-specific information, often at a lower spatial resolution. Effectively combining these two modalities therefore requires an accurate model for their cross-modal relationship. In this work, we propose a multimodal X-ray ptychography and fluorescence reconstruction framework based on physically informed link functions. Rather than relying on a crude linear approximation between the ptychographic object and the fluorescence maps, our approach uses physically motivated link functions to capture the underlying nonlinear coupling between the two imaging modalities. This improved coupling leads to better joint reconstruction quality and more faithful recovery of both structural and compositional features. Numerical experiments on synthetic phantoms and standard test cases demonstrate that the proposed method improves reconstruction accuracy over simpler linking strategies.

Table of Contents

1.Introduction ................................................................ 1

2.Background ................................................................. 4

2.1 Mathematical Formulation .................................... 4

2.2 Linear Link function ............................................ 6

2.3 Gradient and Hessian .......................................... 7

2.3.1 Object Jacobian and Gradient Derivation ....... 7

2.3.2 Object Hessian Derivation ............................. 9

3.Approach .................................................................. 11

3.1 Alternating Optimization Structure .................... 11

3.2 Plug-and-Play (PnP) Framework ...................... 12

3.3 Physical Informed Basis Functions ................... 13

3.4 Patch-based U-Net and Inference .................... 15

4.Experiments .............................................................. 19

4.1 Nonlinear Link Simulation ................................ 23

4.1.1 Noisy Case .................................................. 25

4.1.2 Noiseless Case ............................................. 26

4.1.3 Cameraman/Baboon Case ............................. 30

5.Conclusion ............................................................... 36

Bibliography ................................................................. 38

About this Honors Thesis

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School	Emory College
Department	Mathematics
Degree	B.S.
Submission	Honors Thesis
Language	English
Research Field	Artificial Intelligence Physics, Optics Mathematics
Keyword	Imaging Inverse Problems
Committee Chair / Thesis Advisor	Yuanzhe Xi, Emory University
Committee Members	Kevin Mcalister, Emory University Alessandro Veneziani, Emory University

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