# Deep Learning-Based Solvability of Underdetermined Inverse Problems in Medical Imaging

arXiv: https://arxiv.org/abs/2001.01432 · HTML: https://mlsanity.com/paper/2001.01432/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jan 2020.

## Built on by (most cited first, 14 of 14)

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- [NeRF Solves Undersampled MRI Reconstruction](https://mlsanity.com/paper/2402.13226/) (2024)
- [Metal Artifact Reduction with Intra-Oral Scan Data for 3D Low Dose Maxillofacial CBCT Modeling](https://mlsanity.com/paper/2202.03571/) (2022)
- [LMPDNet: TOF-PET list-mode image reconstruction using model-based deep learning method](https://mlsanity.com/paper/2302.10481/) (2023)
- [Multi-Modal Learning-based Reconstruction of High-Resolution Spatial Wind Speed Fields](https://mlsanity.com/paper/2312.08933/) (2023)
- [An incremental algorithm for non-convex AI-enhanced medical image processing](https://mlsanity.com/paper/2505.08324/) (2025)
- [Adaptive regularization parameter selection for high-dimensional inverse problems: A Bayesian approach with Tucker low-rank constraints](https://mlsanity.com/paper/2603.16066/) (2026)
- [Measurement Geometry and Design for Trustworthy Generative Inverse Problems](https://mlsanity.com/paper/2606.02309/) (2026)

## Abstract (arXiv)

Recently, with the significant developments in deep learning techniques, solving underdetermined inverse problems has become one of the major concerns in the medical imaging domain. Typical examples include undersampled magnetic resonance imaging, interior tomography, and sparse-view computed tomography, where deep learning techniques have achieved excellent performances. Although deep learning methods appear to overcome the limitations of existing mathematical methods when handling various underdetermined problems, there is a lack of rigorous mathematical foundations that would allow us to elucidate the reasons for the remarkable performance of deep learning methods. This study focuses on learning the causal relationship regarding the structure of the training data suitable for deep learning, to solve highly underdetermined inverse problems. We observe that a majority of the problems of solving underdetermined linear systems in medical imaging are highly non-linear. Furthermore, we analyze if a desired reconstruction map can be learnable from the training data and underdetermined system.