# Super-Resolution with Deep Convolutional Sufficient Statistics

arXiv: https://arxiv.org/abs/1511.05666 · HTML: https://mlsanity.com/paper/1511.05666/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Nov 2015.

## Built on by (most cited first, 30 of 35)

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- [PGDiff: Guiding Diffusion Models for Versatile Face Restoration via Partial Guidance](https://mlsanity.com/paper/2309.10810/) (2023)
- [Local Implicit Normalizing Flow for Arbitrary-Scale Image Super-Resolution](https://mlsanity.com/paper/2303.05156/) (2023)
- [Image Compression with Product Quantized Masked Image Modeling](https://mlsanity.com/paper/2212.07372/) (2022)
- [Best-Buddy GANs for Highly Detailed Image Super-Resolution](https://mlsanity.com/paper/2103.15295/) (2021)
- [Memory-augmented Deep Unfolding Network for Guided Image Super-resolution](https://mlsanity.com/paper/2203.04960/) (2022)
- [Latent Space Super-Resolution for Higher-Resolution Image Generation with Diffusion Models](https://mlsanity.com/paper/2503.18446/) (2025)
- [Beyond Image Super-Resolution for Image Recognition with Task-Driven Perceptual Loss](https://mlsanity.com/paper/2404.01692/) (2024)
- [LLDiffusion: Learning Degradation Representations in Diffusion Models for Low-Light Image Enhancement](https://mlsanity.com/paper/2307.14659/) (2023)
- [Perceptual Loss for Robust Unsupervised Homography Estimation](https://mlsanity.com/paper/2104.10011/) (2021)
- [RankSRGAN: Super Resolution Generative Adversarial Networks with Learning to Rank](https://mlsanity.com/paper/2107.09427/) (2021)
- [A Kinematic Bottleneck Approach For Pose Regression of Flexible Surgical Instruments directly from Images](https://mlsanity.com/paper/2103.00586/) (2021)
- [A Mixed-Supervision Multilevel GAN Framework for Image Quality Enhancement](https://mlsanity.com/paper/2106.15575/) (2021)
- [Flexible Style Image Super-Resolution using Conditional Objective](https://mlsanity.com/paper/2201.04898/) (2022)
- [Blind Motion Deblurring with Pixel-Wise Kernel Estimation via Kernel Prediction Networks](https://mlsanity.com/paper/2308.02947/) (2023)
- [Boosting Flow-based Generative Super-Resolution Models via Learned Prior](https://mlsanity.com/paper/2403.10988/) (2024)
- [Hallucination Score: Towards Mitigating Hallucinations in Generative Image Super-Resolution](https://mlsanity.com/paper/2507.14367/) (2025)
- [Revisiting L1 Loss in Super-Resolution: A Probabilistic View and Beyond](https://mlsanity.com/paper/2201.10084/) (2022)
- [Dual Perceptual Loss for Single Image Super-Resolution Using ESRGAN](https://mlsanity.com/paper/2201.06383/) (2022)
- [Wavelet-based Loss for High-frequency Interface Dynamics](https://mlsanity.com/paper/2209.02316/) (2022)
- [Suppressing Uncertainties in Degradation Estimation for Blind Super-Resolution](https://mlsanity.com/paper/2406.16459/) (2024)
- [Frequency Aware Face Hallucination Generative Adversarial Network with Semantic Structural Constraint](https://mlsanity.com/paper/2110.01880/) (2021)
- [PixelPyramids: Exact Inference Models from Lossless Image Pyramids](https://mlsanity.com/paper/2110.08787/) (2021)
- [Blur2seq: Blind Deblurring and Camera Trajectory Estimation from a Single Camera Motion-blurred Image](https://mlsanity.com/paper/2510.20539/) (2025)
- [Single MR Image Super-Resolution using Generative Adversarial Network](https://mlsanity.com/paper/2207.08036/) (2022)
- [SRTGAN: Triplet Loss based Generative Adversarial Network for Real-World Super-Resolution](https://mlsanity.com/paper/2211.12180/) (2022)

## Abstract (arXiv)

Inverse problems in image and audio, and super-resolution in particular, can be seen as high-dimensional structured prediction problems, where the goal is to characterize the conditional distribution of a high-resolution output given its low-resolution corrupted observation. When the scaling ratio is small, point estimates achieve impressive performance, but soon they suffer from the regression-to-the-mean problem, result of their inability to capture the multi-modality of this conditional distribution. Modeling high-dimensional image and audio distributions is a hard task, requiring both the ability to model complex geometrical structures and textured regions. In this paper, we propose to use as conditional model a Gibbs distribution, where its sufficient statistics are given by deep convolutional neural networks. The features computed by the network are stable to local deformation, and have reduced variance when the input is a stationary texture. These properties imply that the resulting sufficient statistics minimize the uncertainty of the target signals given the degraded observations, while being highly informative. The filters of the CNN are initialized by multiscale complex wavelets, and then we propose an algorithm to fine-tune them by estimating the gradient of the conditional log-likelihood, which bears some similarities with Generative Adversarial Networks. We evaluate experimentally the proposed approach in the image super-resolution task, but the approach is general and could be used in other challenging ill-posed problems such as audio bandwidth extension.