Mathematical Foundations of Deep Learning for Imaging

Dear Colleagues,

Deep learning has had a profound impact on computational imaging, offering powerful new methodologies for solving inverse problems in image reconstruction. Modern approaches leverage data-driven representations to address long-standing challenges such as sparse sampling, limited-angle acquisition, low-dose imaging, and the mitigation of complex artifacts. Yet, despite their impressive empirical success, many of these methods still lack a rigorous theoretical foundation. Questions of stability, reliability, interpretability, and the integration of learned components with classical reconstruction and regularization techniques are becoming increasingly central—both for scientific understanding and for trustworthy deployment in real-world imaging systems.

This Special Issue aims to highlight advances at the intersection of deep learning, inverse problems, and mathematical imaging. We invite contributions that develop and deepen the mathematical theory underpinning modern learning-based imaging methods. Submissions addressing the following topics are particularly welcome:

• Inverse problems and regularization theory for learned reconstruction methods;
• Representation and approximation theory relevant to neural networks and data-driven priors;
• Hybrid reconstruction algorithms that combine physical forward models with learnable components;
• Stability, robustness, and error analysis of deep learning–based reconstruction schemes;
• Optimization and training methodologies, including fine-tuning strategies and architecture design informed by mathematical principles;
• Reliability and trustworthiness of AI methods, including frameworks to mitigate hallucinations and ensure predictable behavior;
• Applications demonstrating mathematically grounded approaches to CT, MRI, PET, ultrasound, and related imaging modalities.

Prof. Dr. Jürgen Frikel
Guest Editor

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