# Solving Inverse Problems with Hybrid Deep Image Priors: the challenge of preventing overfitting

arXiv: https://arxiv.org/abs/2011.01748 · HTML: https://mlsanity.com/paper/2011.01748/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2020.

## Built on by (most cited first, 18 of 18)

- [Language Models are Injective and Hence Invertible](https://mlsanity.com/paper/2510.15511/) (2025)
- [Self-Validation: Early Stopping for Single-Instance Deep Generative Priors](https://mlsanity.com/paper/2110.12271/) (2021)
- [Deep Internal Learning: Deep Learning from a Single Input](https://mlsanity.com/paper/2312.07425/) (2023)
- [Image Restoration by Deep Projected GSURE](https://mlsanity.com/paper/2102.02485/) (2021)
- [Equivariant Imaging for Self-supervised Hyperspectral Image Inpainting](https://mlsanity.com/paper/2404.13159/) (2024)
- [Bagged Deep Image Prior for Recovering Images in the Presence of Speckle Noise](https://mlsanity.com/paper/2402.15635/) (2024)
- [Multilook Coherent Imaging: Theoretical Guarantees and Algorithms](https://mlsanity.com/paper/2505.23594/) (2025)
- [Single-Shot Plug-and-Play Methods for Inverse Problems](https://mlsanity.com/paper/2311.13682/) (2023)
- [You KAN Do It in a Single Shot: Plug-and-Play Methods with Single-Instance Priors](https://mlsanity.com/paper/2412.06204/) (2024)
- [MCDIP-ADMM: Overcoming Overfitting in DIP-based CT reconstruction](https://mlsanity.com/paper/2304.03895/) (2023)
- [Self-Supervised Hyperspectral Inpainting with the Optimisation inspired Deep Neural Network Prior](https://mlsanity.com/paper/2306.07308/) (2023)
- [Self-supervised Deep Hyperspectral Inpainting with the Sparsity and Low-Rank Considerations](https://mlsanity.com/paper/2306.08128/) (2023)
- [Self-supervised Deep Hyperspectral Inpainting with the Plug and Play and Deep Image Prior Models](https://mlsanity.com/paper/2501.08195/) (2025)
- [Deep Spectral Prior](https://mlsanity.com/paper/2505.19873/) (2025)
- [Fast Equivariant Imaging: Accelerating Unsupervised Learning and Model Adaptation via Inexact Splitting](https://mlsanity.com/paper/2507.06764/) (2025)
- [Automating Parameter Selection in Deep Image Prior for Fluorescence Microscopy Image Denoising via Similarity-Based Parameter Transfer](https://mlsanity.com/paper/2601.12055/) (2026)
- [Pooling-Based Context Modeling for Convolution-Free Deep Image Prior](https://mlsanity.com/paper/2607.02952/) (2026)
- [Hyperspectral Diffusion Equivariant Imaging (HyDiff-EI): A Self-supervised Framework for Hyperspectral Image Inpainting](https://mlsanity.com/paper/2608.26812/) (2026)

## Abstract (arXiv)

We mainly analyze and solve the overfitting problem of deep image prior (DIP). Deep image prior can solve inverse problems such as super-resolution, inpainting and denoising. The main advantage of DIP over other deep learning approaches is that it does not need access to a large dataset. However, due to the large number of parameters of the neural network and noisy data, DIP overfits to the noise in the image as the number of iterations grows. In the thesis, we use hybrid deep image priors to avoid overfitting. The hybrid priors are to combine DIP with an explicit prior such as total variation or with an implicit prior such as a denoising algorithm. We use the alternating direction method-of-multipliers (ADMM) to incorporate the new prior and try different forms of ADMM to avoid extra computation caused by the inner loop of ADMM steps. We also study the relation between the dynamics of gradient descent, and the overfitting phenomenon. The numerical results show the hybrid priors play an important role in preventing overfitting. Besides, we try to fit the image along some directions and find this method can reduce overfitting when the noise level is large. When the noise level is small, it does not considerably reduce the overfitting problem.