# Image Restoration by Deep Projected GSURE

arXiv: https://arxiv.org/abs/2102.02485 · HTML: https://mlsanity.com/paper/2102.02485/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 53 references that are in the map.
- First posted on arXiv 4 Feb 2021.

## Builds on (most cited first, 30 of 34)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Deep Multi-scale Convolutional Neural Network for Dynamic Scene Deblurring](https://mlsanity.com/paper/1612.02177/) (2016)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [SinGAN: Learning a Generative Model from a Single Natural Image](https://mlsanity.com/paper/1905.01164/) (2019)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- ["Zero-Shot" Super-Resolution using Deep Internal Learning](https://mlsanity.com/paper/1712.06087/) (2017)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [Learning a Convolutional Neural Network for Non-uniform Motion Blur Removal](https://mlsanity.com/paper/1503.00593/) (2015)
- [Theoretical insights into the optimization landscape of over-parameterized shallow neural networks](https://mlsanity.com/paper/1707.04926/) (2017)
- [Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks](https://mlsanity.com/paper/1810.03982/) (2018)
- ["Double-DIP": Unsupervised Image Decomposition via Coupled Deep-Image-Priors](https://mlsanity.com/paper/1812.00467/) (2018)
- [Deep Geometric Prior for Surface Reconstruction](https://mlsanity.com/paper/1811.10943/) (2018)
- [Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems](https://mlsanity.com/paper/1704.03488/) (2017)
- [DeepRED: Deep Image Prior Powered by RED](https://mlsanity.com/paper/1903.10176/) (2019)
- [From Denoising to Compressed Sensing](https://mlsanity.com/paper/1406.4175/) (2014)
- [Non-Stationary Texture Synthesis by Adversarial Expansion](https://mlsanity.com/paper/1805.04487/) (2018)
- [Learned D-AMP: Principled Neural Network based Compressive Image Recovery](https://mlsanity.com/paper/1704.06625/) (2017)
- [Image Restoration using Total Variation Regularized Deep Image Prior](https://mlsanity.com/paper/1810.12864/) (2018)
- [Test-Time Training with Self-Supervision for Generalization under Distribution Shifts](https://mlsanity.com/paper/1909.13231/) (2019)
- [A Bayesian Perspective on the Deep Image Prior](https://mlsanity.com/paper/1904.07457/) (2019)
- [Unsupervised Learning with Stein's Unbiased Risk Estimator](https://mlsanity.com/paper/1805.10531/) (2018)
- [Training Deep Learning Based Denoisers without Ground Truth Data](https://mlsanity.com/paper/1803.01314/) (2018)
- [Point2Mesh: A Self-Prior for Deformable Meshes](https://mlsanity.com/paper/2005.11084/) (2020)
- [Correction Filter for Single Image Super-Resolution: Robustifying Off-the-Shelf Deep Super-Resolvers](https://mlsanity.com/paper/1912.00157/) (2019)
- [Solving Inverse Problems with Hybrid Deep Image Priors: the challenge of preventing overfitting](https://mlsanity.com/paper/2011.01748/) (2020)
- [Training deep learning based image denoisers from undersampled measurements without ground truth and without image prior](https://mlsanity.com/paper/1806.00961/) (2018)

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

- [GSURE-Based Diffusion Model Training with Corrupted Data](https://mlsanity.com/paper/2305.13128/) (2023)
- [ADIR: Adaptive Diffusion for Image Reconstruction](https://mlsanity.com/paper/2212.03221/) (2022)
- [Deep Internal Learning: Deep Learning from a Single Input](https://mlsanity.com/paper/2312.07425/) (2023)
- [Blind Image Deconvolution Using Variational Deep Image Prior](https://mlsanity.com/paper/2202.00179/) (2022)
- [No-Clean-Reference Image Super-Resolution: Application to Electron Microscopy](https://mlsanity.com/paper/2401.08115/) (2024)
- [SVD-DIP: Overcoming the Overfitting Problem in DIP-based CT Reconstruction](https://mlsanity.com/paper/2303.15748/) (2023)
- [Adaptive Selection of Sampling-Reconstruction in Fourier Compressed Sensing](https://mlsanity.com/paper/2409.11738/) (2024)
- [Anatomical Token Uncertainty for Transformer-Guided Active MRI Acquisition](https://mlsanity.com/paper/2603.21806/) (2026)

## Abstract (arXiv)

Ill-posed inverse problems appear in many image processing applications, such as deblurring and super-resolution. In recent years, solutions that are based on deep Convolutional Neural Networks (CNNs) have shown great promise. Yet, most of these techniques, which train CNNs using external data, are restricted to the observation models that have been used in the training phase. A recent alternative that does not have this drawback relies on learning the target image using internal learning. One such prominent example is the Deep Image Prior (DIP) technique that trains a network directly on the input image with a least-squares loss. In this paper, we propose a new image restoration framework that is based on minimizing a loss function that includes a "projected-version" of the Generalized SteinUnbiased Risk Estimator (GSURE) and parameterization of the latent image by a CNN. We demonstrate two ways to use our framework. In the first one, where no explicit prior is used, we show that the proposed approach outperforms other internal learning methods, such as DIP. In the second one, we show that our GSURE-based loss leads to improved performance when used within a plug-and-play priors scheme.