用仿射子空间建模图像块，提升去噪精度。
Affine Subspace Models and Clustering for Patch-Based Image Denoising
- 以仿射子空间代替线性子空间，更贴合图像块的非负特性。
- 基于最小二乘投影的简单去噪算法，显著改善聚类与去噪效果。
- 适合需要高精度图像重建的应用，如医学影像处理。
基于图像块的方法在去噪等图像处理任务中广泛应用（如非局部均值）。其关键步骤是将图像分组聚类，通常通过迭代分割和每簇模型拟合实现。线性子空间常被用于建模图像块簇，但因其假设数据围绕原点分布，难以匹配图像块向量空间中非负的实际结构。本文研究使用仿射子空间模型来更好地刻画图像块的几何特征。提出一种基于最小二乘投影的简单去噪算法，依赖仿射子空间聚类模型。综述多种求解仿射子空间聚类问题的算法，并通过实验验证其在聚类和去噪性能上的提升。
原文摘要 · Abstract (English)
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.
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