# A Bayesian Perspective on the Deep Image Prior

arXiv: https://arxiv.org/abs/1904.07457 · HTML: https://mlsanity.com/paper/1904.07457/

## Key facts

- Cited by 52 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Apr 2019.

## Built on by (most cited first, 30 of 52)

- [Early Stopping for Deep Image Prior](https://mlsanity.com/paper/2112.06074/) (2021)
- [Rethinking Deep Image Prior for Denoising](https://mlsanity.com/paper/2108.12841/) (2021)
- [On Measuring and Controlling the Spectral Bias of the Deep Image Prior](https://mlsanity.com/paper/2107.01125/) (2021)
- [A Survey on Epistemic (Model) Uncertainty in Supervised Learning: Recent Advances and Applications](https://mlsanity.com/paper/2111.01968/) (2021)
- [NCP: Neural Correspondence Prior for Effective Unsupervised Shape Matching](https://mlsanity.com/paper/2301.05839/) (2023)
- [Simple, Fast, and Flexible Framework for Matrix Completion with Infinite Width Neural Networks](https://mlsanity.com/paper/2108.00131/) (2021)
- [An Educated Warm Start For Deep Image Prior-Based Micro CT Reconstruction](https://mlsanity.com/paper/2111.11926/) (2021)
- [Self-Validation: Early Stopping for Single-Instance Deep Generative Priors](https://mlsanity.com/paper/2110.12271/) (2021)
- [GI-NAS: Boosting Gradient Inversion Attacks Through Adaptive Neural Architecture Search](https://mlsanity.com/paper/2405.20725/) (2024)
- [A review and experimental evaluation of deep learning methods for MRI reconstruction](https://mlsanity.com/paper/2109.08618/) (2021)
- [Deep Bayesian inference for seismic imaging with tasks](https://mlsanity.com/paper/2110.04825/) (2021)
- [The Devil is in the Upsampling: Architectural Decisions Made Simpler for Denoising with Deep Image Prior](https://mlsanity.com/paper/2304.11409/) (2023)
- [Analysis of Deep Image Prior and Exploiting Self-Guidance for Image Reconstruction](https://mlsanity.com/paper/2402.04097/) (2024)
- [Uncertainty Estimation for Computed Tomography with a Linearised Deep Image Prior](https://mlsanity.com/paper/2203.00479/) (2022)
- [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)
- [Unsupervised Shape Completion via Deep Prior in the Neural Tangent Kernel Perspective](https://mlsanity.com/paper/2104.09023/) (2021)
- [Faster Kernel Interpolation for Gaussian Processes](https://mlsanity.com/paper/2101.11751/) (2021)
- [Posterior Sampling for Image Restoration using Explicit Patch Priors](https://mlsanity.com/paper/2104.09895/) (2021)
- [Equilibrated Zeroth-Order Unrolled Deep Networks for Accelerated MRI](https://mlsanity.com/paper/2112.09891/) (2021)
- [Blind Image Deconvolution Using Variational Deep Image Prior](https://mlsanity.com/paper/2202.00179/) (2022)
- [Discovering Structure From Corruption for Unsupervised Image Reconstruction](https://mlsanity.com/paper/2304.05589/) (2023)
- [NPBDREG: Uncertainty Assessment in Diffeomorphic Brain MRI Registration using a Non-parametric Bayesian Deep-Learning Based Approach](https://mlsanity.com/paper/2108.06771/) (2021)
- [Self-Supervised Pre-Training for Deep Image Prior-Based Robust PET Image Denoising](https://mlsanity.com/paper/2302.13546/) (2023)
- [NPB-REC: A Non-parametric Bayesian Deep-learning Approach for Undersampled MRI Reconstruction with Uncertainty Estimation](https://mlsanity.com/paper/2404.04550/) (2024)
- [Posterior Temperature Optimization in Variational Inference for Inverse Problems](https://mlsanity.com/paper/2106.07533/) (2021)
- [Posterior temperature optimized Bayesian models for inverse problems in medical imaging](https://mlsanity.com/paper/2202.00986/) (2022)
- [Priors in Deep Image Restoration and Enhancement: A Survey](https://mlsanity.com/paper/2206.02070/) (2022)
- [Towards Architecture-Agnostic Untrained Network Priors for Image Reconstruction with Frequency Regularization](https://mlsanity.com/paper/2312.09988/) (2023)
- [Unsupervised Training of Convex Regularizers using Maximum Likelihood Estimation](https://mlsanity.com/paper/2404.05445/) (2024)

## Abstract (arXiv)

The deep image prior was recently introduced as a prior for natural images. It represents images as the output of a convolutional network with random inputs. For "inference", gradient descent is performed to adjust network parameters to make the output match observations. This approach yields good performance on a range of image reconstruction tasks. We show that the deep image prior is asymptotically equivalent to a stationary Gaussian process prior in the limit as the number of channels in each layer of the network goes to infinity, and derive the corresponding kernel. This informs a Bayesian approach to inference. We show that by conducting posterior inference using stochastic gradient Langevin we avoid the need for early stopping, which is a drawback of the current approach, and improve results for denoising and impainting tasks. We illustrate these intuitions on a number of 1D and 2D signal reconstruction tasks.