# Image Restoration and Reconstruction using Variable Splitting and Class-adapted Image Priors

arXiv: https://arxiv.org/abs/1602.04052 · HTML: https://mlsanity.com/paper/1602.04052/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2016.

## Built on by (most cited first, 5 of 5)

- [Deep Generalized Unfolding Networks for Image Restoration](https://mlsanity.com/paper/2204.13348/) (2022)
- [Denoising: A Powerful Building-Block for Imaging, Inverse Problems, and Machine Learning](https://mlsanity.com/paper/2409.06219/) (2024)
- [Taking a Big Step: Large Learning Rates in Denoising Score Matching Prevent Memorization](https://mlsanity.com/paper/2502.03435/) (2025)
- [Single-Shot Plug-and-Play Methods for Inverse Problems](https://mlsanity.com/paper/2311.13682/) (2023)
- [Spherical Image Inpainting with Frame Transformation and Data-driven Prior Deep Networks](https://mlsanity.com/paper/2209.14604/) (2022)

## Abstract (arXiv)

This paper proposes using a Gaussian mixture model as a prior, for solving two image inverse problems, namely image deblurring and compressive imaging. We capitalize on the fact that variable splitting algorithms, like ADMM, are able to decouple the handling of the observation operator from that of the regularizer, and plug a state-of-the-art algorithm into the pure denoising step. Furthermore, we show that, when applied to a specific type of image, a Gaussian mixture model trained from an database of images of the same type is able to outperform current state-of-the-art methods.