# Sparsity Based Poisson Denoising with Dictionary Learning

arXiv: https://arxiv.org/abs/1309.4306 · HTML: https://mlsanity.com/paper/1309.4306/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2013.

## Built on by (most cited first, 9 of 9)

- [Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --](https://mlsanity.com/paper/2301.03362/) (2023)
- [Cross-Modality Neuroimage Synthesis: A Survey](https://mlsanity.com/paper/2202.06997/) (2022)
- [Deep Joint Unrolling for Deblurring and Low-Light Image Enhancement (JUDE)](https://mlsanity.com/paper/2412.07527/) (2024)
- [On Hamilton-Jacobi PDEs and image denoising models with certain non-additive noise](https://mlsanity.com/paper/2105.13997/) (2021)
- [Poisson2Sparse: Self-Supervised Poisson Denoising From a Single Image](https://mlsanity.com/paper/2206.01856/) (2022)
- [Gaussian Process Convolutional Dictionary Learning](https://mlsanity.com/paper/2104.00530/) (2021)
- [Sparse Dictionary Learning for Image Recovery by Iterative Shrinkage](https://mlsanity.com/paper/2503.10732/) (2025)
- [Recognition of Geometrical Shapes by Dictionary Learning](https://mlsanity.com/paper/2504.10958/) (2025)
- [Quality Versus Sparsity in Image Recovery by Dictionary Learning Using Iterative Shrinkage](https://mlsanity.com/paper/2508.03492/) (2025)

## Abstract (arXiv)

The problem of Poisson denoising appears in various imaging applications, such as low-light photography, medical imaging and microscopy. In cases of high SNR, several transformations exist so as to convert the Poisson noise into an additive i.i.d. Gaussian noise, for which many effective algorithms are available. However, in a low SNR regime, these transformations are significantly less accurate, and a strategy that relies directly on the true noise statistics is required. A recent work by Salmon et al. took this route, proposing a patch-based exponential image representation model based on GMM (Gaussian mixture model), leading to state-of-the-art results. In this paper, we propose to harness sparse-representation modeling to the image patches, adopting the same exponential idea. Our scheme uses a greedy pursuit with boot-strapping based stopping condition and dictionary learning within the denoising process. The reconstruction performance of the proposed scheme is competitive with leading methods in high SNR, and achieving state-of-the-art results in cases of low SNR.