# Affine Subspace Models and Clustering for Patch-Based Image Denoising

arXiv: https://arxiv.org/abs/2512.07259 · HTML: https://mlsanity.com/paper/2512.07259/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 40 references that are in the map.
- First posted on arXiv 8 Dec 2025.

## Builds on (most cited first, 11 of 11)

- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [Regularization by Denoising: Clarifications and New Interpretations](https://mlsanity.com/paper/1806.02296/) (2018)
- [Robust subspace clustering](https://mlsanity.com/paper/1301.2603/) (2013)
- [Algorithms for Fitting the Constrained Lasso](https://mlsanity.com/paper/1611.01511/) (2016)
- [On Geometric Analysis of Affine Sparse Subspace Clustering](https://mlsanity.com/paper/1808.05965/) (2018)
- [Is an Affine Constraint Needed for Affine Subspace Clustering?](https://mlsanity.com/paper/2005.03888/) (2020)
- [Convergence and Recovery Guarantees of the K-Subspaces Method for Subspace Clustering](https://mlsanity.com/paper/2206.05553/) (2022)
- [Nonlocal Low-Rank Tensor Factor Analysis for Image Restoration](https://mlsanity.com/paper/1803.06795/) (2018)
- [Probabilistic Non-Local Means](https://mlsanity.com/paper/1302.5762/) (2013)
- [Monte Carlo non local means: Random sampling for large-scale image filtering](https://mlsanity.com/paper/1312.7366/) (2013)

## Abstract (arXiv)

Image tile-based approaches are popular in many image processing applications such as denoising (e.g., non-local means). A key step in their use is grouping the images into clusters, which usually proceeds iteratively splitting the images into clusters and fitting a model for the images in each cluster. Linear subspaces have emerged as a suitable model for tile clusters; however, they are not well matched to images patches given that images are non-negative and thus not distributed around the origin in the tile vector space. We study the use of affine subspace models for the clusters to better match the geometric structure of the image tile vector space. We also present a simple denoising algorithm that relies on the affine subspace clustering model using least squares projection. We review several algorithmic approaches to solve the affine subspace clustering problem and show experimental results that highlight the performance improvements in clustering and denoising.