Principal neighborhood dictionaries for nonlocal means image denoising

We present an in-depth analysis of a variation of the nonlocal means (NLM) image denoising algorithm that uses principal component analysis (PCA) to achieve a higher accuracy while reducing computational load. Image neighborhood vectors are first projected onto a lower dimensional subspace using PCA. The dimensionality of this subspace is chosen automatically using parallel analysis. Consequently, neighborhood similarity weights for denoising are computed using distances in this subspace rather than the full space. The resulting algorithm is referred to as principal neighborhood dictionary (PND) nonlocal means. We investigate PND's accuracy as a function of the dimensionality of the projection subspace and demonstrate that denoising accuracy peaks at a relatively low number of dimensions. The accuracy of NLM and PND are also examined with respect to the choice of image neighborhood and search window sizes. Finally, we present a quantitative and qualitative comparison of PND versus NLM and another image neighborhood PCA-based state-of-the-art image denoising algorithm.