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Regularization by architecture: A deep prior approach for inverse problems

arXiv 1812.03889 ↗First posted 10 Dec 2018cs.LG stat.MLcited by 26

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Abstract (arXiv)

The present paper studies so-called deep image prior (DIP) techniques in the context of ill-posed inverse problems. DIP networks have been recently introduced for applications in image processing; also first experimental results for applying DIP to inverse problems have been reported. This paper aims at discussing different interpretations of DIP and to obtain analytic results for specific network designs and linear operators. The main contribution is to introduce the idea of viewing these approaches as the optimization of Tikhonov functionals rather than optimizing networks. Besides theoretical results, we present numerical verifications.

Key facts. Cited by 26 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Dec 2018.

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Citing papers per year: 2021: 8; 2022: 3; 2023: 3; 2024: 6; 2025: 4; 2026: 2.

26 papers.

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  1. 2022Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problemscited by 34
  2. 2021Regularising Inverse Problems with Generative Machine Learning Modelscited by 22
  3. 2021Learning Regularization Parameters of Inverse Problems via Deep Neural Networkscited by 19
  4. 2023NCP: Neural Correspondence Prior for Effective Unsupervised Shape Matchingcited by 18
  5. 2024Nonlocal Attention Operator: Materializing Hidden Knowledge Towards Interpretable Physics Discoverycited by 18
  6. 2021An Educated Warm Start For Deep Image Prior-Based Micro CT Reconstructioncited by 16
  7. 2021Deep Bayesian inference for seismic imaging with taskscited by 12
  8. 2024Weakly Convex Regularisers for Inverse Problems: Convergence of Critical Points and Primal-Dual Optimisationcited by 12
  9. 2021Unsupervised Knowledge-Transfer for Learned Image Reconstructioncited by 4
  10. 2023An adaptively inexact first-order method for bilevel optimization with application to hyperparameter learningcited by 4
  11. 2024Heterogeneous Peridynamic Neural Operators: Discover Biotissue Constitutive Law and Microstructure From Digital Image Correlation Measurementscited by 4
  12. 2022CNN-based Euler's Elastica Inpainting with Deep Energy and Deep Image Priorcited by 2
14 more
  1. 2023SVD-DIP: Overcoming the Overfitting Problem in DIP-based CT Reconstructioncited by 2
  2. 2024Disentangled Representation Learning for Parametric Partial Differential Equationscited by 2
  3. 2021A Design Space Study for LISTA and Beyondcited by 1
  4. 2021Survey of Deep Learning Methods for Inverse Problemscited by 1
  5. 2022K-UNN: k-Space Interpolation With Untrained Neural Networkcited by 1
  6. 2024Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overviewcited by 1
  7. 2024SDIP: Self-Reinforcement Deep Image Prior Framework for Image Processingcited by 1
  8. 2025Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discoverycited by 1
  9. 2025Unsupervised Deep Learning for Inverse Problems in Computed Tomographycited by 1
  10. 2025Geometric Autoencoder Priors for Bayesian Inversion: Learn First Observe Latercited by 1
  11. 2021Deformable image registration with deep network priors: a study on longitudinal PET imagescited by 0
  12. 2025Optimization Landscapes Learned: Proxy Networks Boost Convergence in Physics-based Inverse Problemscited by 0
  13. 2026Deep Image Prior for photoacoustic tomography can mitigate limited-view artifactscited by 0
  14. 2026GAIA: Geometry-Adaptive Operator Learning for Forward and Inverse Problemscited by 0