# Regularization by architecture: A deep prior approach for inverse problems

arXiv: https://arxiv.org/abs/1812.03889 · HTML: https://mlsanity.com/paper/1812.03889/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Dec 2018.

## Built on by (most cited first, 26 of 26)

- [Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problems](https://mlsanity.com/paper/2212.03130/) (2022)
- [Regularising Inverse Problems with Generative Machine Learning Models](https://mlsanity.com/paper/2107.11191/) (2021)
- [Learning Regularization Parameters of Inverse Problems via Deep Neural Networks](https://mlsanity.com/paper/2104.06594/) (2021)
- [NCP: Neural Correspondence Prior for Effective Unsupervised Shape Matching](https://mlsanity.com/paper/2301.05839/) (2023)
- [Nonlocal Attention Operator: Materializing Hidden Knowledge Towards Interpretable Physics Discovery](https://mlsanity.com/paper/2408.07307/) (2024)
- [An Educated Warm Start For Deep Image Prior-Based Micro CT Reconstruction](https://mlsanity.com/paper/2111.11926/) (2021)
- [Weakly Convex Regularisers for Inverse Problems: Convergence of Critical Points and Primal-Dual Optimisation](https://mlsanity.com/paper/2402.01052/) (2024)
- [Deep Bayesian inference for seismic imaging with tasks](https://mlsanity.com/paper/2110.04825/) (2021)
- [Unsupervised Knowledge-Transfer for Learned Image Reconstruction](https://mlsanity.com/paper/2107.02572/) (2021)
- [An adaptively inexact first-order method for bilevel optimization with application to hyperparameter learning](https://mlsanity.com/paper/2308.10098/) (2023)
- [Heterogeneous Peridynamic Neural Operators: Discover Biotissue Constitutive Law and Microstructure From Digital Image Correlation Measurements](https://mlsanity.com/paper/2403.18597/) (2024)
- [Disentangled Representation Learning for Parametric Partial Differential Equations](https://mlsanity.com/paper/2410.02136/) (2024)
- [CNN-based Euler's Elastica Inpainting with Deep Energy and Deep Image Prior](https://mlsanity.com/paper/2207.07921/) (2022)
- [SVD-DIP: Overcoming the Overfitting Problem in DIP-based CT Reconstruction](https://mlsanity.com/paper/2303.15748/) (2023)
- [Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery](https://mlsanity.com/paper/2505.23106/) (2025)
- [A Design Space Study for LISTA and Beyond](https://mlsanity.com/paper/2104.04110/) (2021)
- [Survey of Deep Learning Methods for Inverse Problems](https://mlsanity.com/paper/2111.04731/) (2021)
- [K-UNN: k-Space Interpolation With Untrained Neural Network](https://mlsanity.com/paper/2208.05827/) (2022)
- [Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overview](https://mlsanity.com/paper/2402.12072/) (2024)
- [SDIP: Self-Reinforcement Deep Image Prior Framework for Image Processing](https://mlsanity.com/paper/2404.12142/) (2024)
- [Unsupervised Deep Learning for Inverse Problems in Computed Tomography](https://mlsanity.com/paper/2508.05321/) (2025)
- [Geometric Autoencoder Priors for Bayesian Inversion: Learn First Observe Later](https://mlsanity.com/paper/2509.19929/) (2025)
- [GAIA: Geometry-Adaptive Operator Learning for Forward and Inverse Problems](https://mlsanity.com/paper/2607.01128/) (2026)
- [Deformable image registration with deep network priors: a study on longitudinal PET images](https://mlsanity.com/paper/2111.11873/) (2021)
- [Optimization Landscapes Learned: Proxy Networks Boost Convergence in Physics-based Inverse Problems](https://mlsanity.com/paper/2501.16573/) (2025)
- [Deep Image Prior for photoacoustic tomography can mitigate limited-view artifacts](https://mlsanity.com/paper/2604.19176/) (2026)

## 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.