# Image Restoration using Autoencoding Priors

arXiv: https://arxiv.org/abs/1703.09964 · HTML: https://mlsanity.com/paper/1703.09964/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Mar 2017.

## Built on by (most cited first, 8 of 8)

- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Gradient Step Denoiser for convergent Plug-and-Play](https://mlsanity.com/paper/2110.03220/) (2021)
- [Solving Inverse Problems by Joint Posterior Maximization with Autoencoding Prior](https://mlsanity.com/paper/2103.01648/) (2021)
- [Learning Regularization Functionals for Inverse Problems: A Comparative Study](https://mlsanity.com/paper/2510.01755/) (2025)
- [MeanShift++: Extremely Fast Mode-Seeking With Applications to Segmentation and Object Tracking](https://mlsanity.com/paper/2104.00303/) (2021)
- [DiffuseRAW: End-to-End Generative RAW Image Processing for Low-Light Images](https://mlsanity.com/paper/2402.18575/) (2023)
- [Real-World Adverse Weather Image Restoration via Dual-Level Reinforcement Learning with High-Quality Cold Start](https://mlsanity.com/paper/2511.05095/) (2025)
- [Incomplete Gamma Kernels: Generalizing Locally Optimal Projection Operators](https://mlsanity.com/paper/2205.01087/) (2022)

## Abstract (arXiv)

We propose to leverage denoising autoencoder networks as priors to address image restoration problems. We build on the key observation that the output of an optimal denoising autoencoder is a local mean of the true data density, and the autoencoder error (the difference between the output and input of the trained autoencoder) is a mean shift vector. We use the magnitude of this mean shift vector, that is, the distance to the local mean, as the negative log likelihood of our natural image prior. For image restoration, we maximize the likelihood using gradient descent by backpropagating the autoencoder error. A key advantage of our approach is that we do not need to train separate networks for different image restoration tasks, such as non-blind deconvolution with different kernels, or super-resolution at different magnification factors. We demonstrate state of the art results for non-blind deconvolution and super-resolution using the same autoencoding prior.