# Weighted Anisotropic-Isotropic Total Variation for Poisson Denoising

arXiv: https://arxiv.org/abs/2307.00439 · HTML: https://mlsanity.com/paper/2307.00439/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 29 references that are in the map.
- First posted on arXiv 1 Jul 2023.

## Builds on (most cited first, 6 of 6)

- [Global Convergence of ADMM in Nonconvex Nonsmooth Optimization](https://mlsanity.com/paper/1511.06324/) (2015)
- [Adaptive Unfolding Total Variation Network for Low-Light Image Enhancement](https://mlsanity.com/paper/2110.00984/) (2021)
- [Fast L1-L2 minimization via a proximal operator](https://mlsanity.com/paper/1609.09530/) (2016)
- [Class-Aware Fully-Convolutional Gaussian and Poisson Denoising](https://mlsanity.com/paper/1808.06562/) (2018)
- [From Rank Estimation to Rank Approximation: Rank Residual Constraint for Image Restoration](https://mlsanity.com/paper/1807.02504/) (2018)
- [DN-ResNet: Efficient Deep Residual Network for Image Denoising](https://mlsanity.com/paper/1810.06766/) (2018)

## Built on by (most cited first, 3 of 3)

- [DocVXQA: Context-Aware Visual Explanations for Document Question Answering](https://mlsanity.com/paper/2505.07496/) (2025)
- [Negative Binomial Matrix Completion](https://mlsanity.com/paper/2408.16113/) (2024)
- [Alternating Direction Method of Multipliers for Negative Binomial Model with The Weighted Difference of Anisotropic and Isotropic Total Variation](https://mlsanity.com/paper/2408.16117/) (2024)

## Abstract (arXiv)

Poisson noise commonly occurs in images captured by photon-limited imaging systems such as in astronomy and medicine. As the distribution of Poisson noise depends on the pixel intensity value, noise levels vary from pixels to pixels. Hence, denoising a Poisson-corrupted image while preserving important details can be challenging. In this paper, we propose a Poisson denoising model by incorporating the weighted anisotropic-isotropic total variation (AITV) as a regularization. We then develop an alternating direction method of multipliers with a combination of a proximal operator for an efficient implementation. Lastly, numerical experiments demonstrate that our algorithm outperforms other Poisson denoising methods in terms of image quality and computational efficiency.