Affine Subspace Models and Clustering for Patch-Based Image Denoising

TL;DR

Affine Subspace Models and Clustering for Patch-Based Image Denoising proposes using affine subspaces to model image patches, addressing non-negativity that makes zero-mean linear subspaces suboptimal. It develops self-representation-based clustering with affine constraints, including three variants (BPDN, NNC lasso, NN lasso) to build affinity matrices for spectral clustering. The authors integrate this clustering into a simple patch-subspace projection denoising (PSP) method, which projects noisy patches onto the learned affine subspaces, using mean subtraction and PCA. Experimental results demonstrate improved clustering structure and superior denoising performance against non-local means, especially when affineness is enforced.

Abstract

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.

Figures (4)

• Figure 1: Denoising example results for Cameraman image: original, noisy, and denoised images for each of the methods: BPDN, NC-Lasso, and NNC-Lasso. The noisy image has additive gaussian noise with $\sigma = 20$ pixels. Non-Local-Means (NLM) uses an estimate of the noise $\hat{\sigma}$ for the filter parameter.
• Figure 2: Clusters obtained from the Cameraman image for two competing methods, including four randomly drawn samples from each cluster. For each cluster, $n$ denotes the number of patches in the cluster. Top: clusters generated using NNC lasso. Bottom: clusters generated using BPDN.
• Figure 3: Denoising comparison of patched affine subspace clustering methods, compared to a baseline NLM algorithm at different noise levels. Evaluations are averaged across all test images.
• Figure 4: Comparison among patched subspace clustering methods. Enforcing the affine constraint through NNC lasso consistently improves the denoising performance across noise levels