# Super-Resolution via Image-Adapted Denoising CNNs: Incorporating External and Internal Learning

arXiv: https://arxiv.org/abs/1811.12866 · HTML: https://mlsanity.com/paper/1811.12866/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2018.

## Built on by (most cited first, 12 of 12)

- [Deep Equilibrium Architectures for Inverse Problems in Imaging](https://mlsanity.com/paper/2102.07944/) (2021)
- [Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidance](https://mlsanity.com/paper/2312.16519/) (2023)
- [ADIR: Adaptive Diffusion for Image Reconstruction](https://mlsanity.com/paper/2212.03221/) (2022)
- [Zero-Shot Image Restoration Using Few-Step Guidance of Consistency Models (and Beyond)](https://mlsanity.com/paper/2412.20596/) (2024)
- [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)
- [CurvPnP: Plug-and-play Blind Image Restoration with Deep Curvature Denoiser](https://mlsanity.com/paper/2211.07286/) (2022)
- [Deep learning architectural designs for super-resolution of noisy images](https://mlsanity.com/paper/2102.05105/) (2021)
- [A hybrid approach to seismic deblending: when physics meets self-supervision](https://mlsanity.com/paper/2205.15395/) (2022)
- [Equivariant Sampling for Improving Diffusion Model-based Image Restoration](https://mlsanity.com/paper/2511.09965/) (2025)
- [An Interpretation of Regularization by Denoising and its Application with the Back-Projected Fidelity Term](https://mlsanity.com/paper/2101.11599/) (2021)
- [Jacobian-Aware Posterior Sampling for Inverse Problems](https://mlsanity.com/paper/2511.18471/) (2025)

## Abstract (arXiv)

While deep neural networks exhibit state-of-the-art results in the task of image super-resolution (SR) with a fixed known acquisition process (e.g., a bicubic downscaling kernel), they experience a huge performance loss when the real observation model mismatches the one used in training. Recently, two different techniques suggested to mitigate this deficiency, i.e., enjoy the advantages of deep learning without being restricted by the training phase. The first one follows the plug-and-play (P&P) approach that solves general inverse problems (e.g., SR) by using Gaussian denoisers for handling the prior term in model-based optimization schemes. The second builds on internal recurrence of information inside a single image, and trains a super-resolver network at test time on examples synthesized from the low-resolution image. Our work incorporates these two independent strategies, enjoying the impressive generalization capabilities of deep learning, captured by the first, and further improving it through internal learning at test time. First, we apply a recent P&P strategy to SR. Then, we show how it may become image-adaptive in test time. This technique outperforms the above two strategies on popular datasets and gives better results than other state-of-the-art methods in practical cases where the observation model is inexact or unknown in advance.