# High-dimensional Assisted Generative Model for Color Image Restoration

arXiv: https://arxiv.org/abs/2108.06460 · HTML: https://mlsanity.com/paper/2108.06460/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 20 of its 56 references that are in the map.
- First posted on arXiv 14 Aug 2021.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 20 of 20)

- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Context Encoders: Feature Learning by Inpainting](https://mlsanity.com/paper/1604.07379/) (2016)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Accurate Image Super-Resolution Using Very Deep Convolutional Networks](https://mlsanity.com/paper/1511.04587/) (2015)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [DRAW: A Recurrent Neural Network For Image Generation](https://mlsanity.com/paper/1502.04623/) (2015)
- [Deep Convolutional Inverse Graphics Network](https://mlsanity.com/paper/1503.03167/) (2015)
- [Generative Modeling with Denoising Auto-Encoders and Langevin Sampling](https://mlsanity.com/paper/2002.00107/) (2020)
- [Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems](https://mlsanity.com/paper/1704.03488/) (2017)
- [Recurrent Feature Reasoning for Image Inpainting](https://mlsanity.com/paper/2008.03737/) (2020)
- [Rethinking Image Inpainting via a Mutual Encoder-Decoder with Feature Equalizations](https://mlsanity.com/paper/2007.06929/) (2020)
- [Generative Face Completion](https://mlsanity.com/paper/1704.05838/) (2017)
- [Perceptual Adversarial Networks for Image-to-Image Transformation](https://mlsanity.com/paper/1706.09138/) (2017)
- [PEPSI++: Fast and Lightweight Network for Image Inpainting](https://mlsanity.com/paper/1905.09010/) (2019)
- [Homotopic Gradients of Generative Density Priors for MR Image Reconstruction](https://mlsanity.com/paper/2008.06284/) (2020)

## Built on by (most cited first, 1 of 1)

- [Low-rank Tensor Assisted K-space Generative Model for Parallel Imaging Reconstruction](https://mlsanity.com/paper/2212.05503/) (2022)

## Abstract (arXiv)

This work presents an unsupervised deep learning scheme that exploiting high-dimensional assisted score-based generative model for color image restoration tasks. Considering that the sample number and internal dimension in score-based generative model have key influence on estimating the gradients of data distribution, two different high-dimensional ways are proposed: The channel-copy transformation increases the sample number and the pixel-scale transformation decreases feasible space dimension. Subsequently, a set of high-dimensional tensors represented by these transformations are used to train the network through denoising score matching. Then, sampling is performed by annealing Langevin dynamics and alternative data-consistency update. Furthermore, to alleviate the difficulty of learning high-dimensional representation, a progressive strategy is proposed to leverage the performance. The proposed unsupervised learning and iterative restoration algo-rithm, which involves a pre-trained generative network to obtain prior, has transparent and clear interpretation compared to other data-driven approaches. Experimental results on demosaicking and inpainting conveyed the remarkable performance and diversity of our proposed method.