Abstract:In clinical applications, X-ray technology is vital for noninvasive examinations like mammography, providing essential anatomical information. However, the radiation risk associated with X-ray procedures raises concerns. X-ray reconstruction is crucial in medical imaging for detailed visual representations of internal structures, aiding diagnosis and treatment without invasive procedures. Recent advancements in deep learning (DL) have shown promise in X-ray reconstruction, but conventional DL methods often require centralized aggregation of large datasets, leading to domain shifts and privacy issues. To address these challenges, we introduce the Hierarchical Framework-based Federated Learning method (HF-Fed) for customized X-ray imaging. HF-Fed tackles X-ray imaging optimization by decomposing the problem into local data adaptation and holistic X-ray imaging. It employs a hospital-specific hierarchical framework and a shared common imaging network called Network of Networks (NoN) to acquire stable features from diverse data distributions. The hierarchical hypernetwork extracts domain-specific hyperparameters, conditioning the NoN for customized X-ray reconstruction. Experimental results demonstrate HF-Fed's competitive performance, offering a promising solution for enhancing X-ray imaging without data sharing. This study significantly contributes to the literature on federated learning in healthcare, providing valuable insights for policymakers and healthcare providers. The source code and pre-trained HF-Fed model are available at \url{https://tisharepo.github.io/Webpage/}.