mlsanityData to 14 Oct 2026

Theoretical Perspectives on Deep Learning Methods in Inverse Problems

arXiv 2206.14373 ↗First posted 29 Jun 2022stat.ML cs.IT cs.LGcited by 22

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Abstract (arXiv)

In recent years, there have been significant advances in the use of deep learning methods in inverse problems such as denoising, compressive sensing, inpainting, and super-resolution. While this line of works has predominantly been driven by practical algorithms and experiments, it has also given rise to a variety of intriguing theoretical problems. In this paper, we survey some of the prominent theoretical developments in this line of works, focusing in particular on generative priors, untrained neural network priors, and unfolding algorithms. In addition to summarizing existing results in these topics, we highlight several ongoing challenges and open problems.

Key facts. Cited by 22 papers in the map (data through 14 Oct 2026). Builds on 98 of its 156 references that are in the map. First posted on arXiv 29 Jun 2022.

Builds on

98 of 156 references.

References · 98

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38 more
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Citing papers per year: 2022: 2; 2023: 5; 2024: 4; 2025: 9; 2026: 2.

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  1. 2024A Survey on Diffusion Models for Inverse Problemscited by 180
  2. 2024Rethinking Visual Counterfactual Explanations Through Region Constraintcited by 14
  3. 2022A coherence parameter characterizing generative compressed sensing with Fourier measurementscited by 8
  4. 2022Misspecified Phase Retrieval with Generative Priorscited by 7
  5. 2023A Unified Framework for Uniform Signal Recovery in Nonlinear Generative Compressed Sensingcited by 7
  6. 2025Deep Unfolding: Recent Developments, Theory, and Design Guidelinescited by 7
  7. 2023Solving Linear Inverse Problems using Higher-Order Annealed Langevin Diffusioncited by 6
  8. 2023Generative adversarial networks with physical sound field priorscited by 4
  9. 2025NPN: Non-Linear Projections of the Null-Space for Imaging Inverse Problemscited by 4
  10. 2023Generalization analysis of an unfolding network for analysis-based Compressed Sensingcited by 2
  11. 2023Uncertainty quantification for learned ISTAcited by 2
  12. 2025How many measurements are enough? Bayesian recovery in inverse problems with general distributionscited by 2
10 more
  1. 2025Deep greedy unfolding: Sorting out argsorting in greedy sparse recovery algorithmscited by 2
  2. 2025Learning Single Index Models with Diffusion Priorscited by 2
  3. 2024Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overviewcited by 1
  4. 2025Predictive posterior sampling from non-stationnary Gaussian process priors via Diffusion models with application to climate datacited by 1
  5. 2025Diffusion Model Based Signal Recovery Under 1-Bit Quantizationcited by 1
  6. 2026Tunable Latent Generative Priors for Compressed Sensing and Inverse Problemscited by 1
  7. 2024Imaging Signal Recovery Using Neural Network Priors Under Uncertain Forward Model Parameterscited by 0
  8. 2025Adversarial generalization of unfolding (model-based) networkscited by 0
  9. 2025Saving Foundation Flow-Matching Priors for Inverse Problemscited by 0
  10. 2026Hallucination-Aware Diffusion Sampling for Inverse Problems via Robust Prior Updatescited by 0