2011/12/19 by Ery Arias-Castro, Arias-Castro, Ery, Joseph Salmon +3 · 1 citation
Computer Science · Mathematics · #Image and Signal Denoising Methods #Neural Networks and Applications #Advanced Statistical Methods and Models
paper · pdf · doi:10.48550/arxiv.1112.4434
This paper describes a novel theoretical characterization of the performance\nof non-local means (NLM) for noise removal. NLM has proven effective in a\nvariety of empirical studies, but little is understood fundamentally about how\nit performs relative to classical methods based on wavelets or how various\nparameters (e.g., patch size) should be chosen. For cartoon images and images\nwhich may contain thin features and regular textures, the error decay rates of\nNLM are derived and compared with those of linear filtering, oracle estimators,\nvariable-bandwidth kernel methods, Yaroslavsky's filter and wavelet\nthresholding estimators. The trade-off between global and local search for\nmatching patches is examined, and the bias reduction associated with the local\npolynomial regression version of NLM is analyzed. The theoretical results are\nvalidated via simulations for 2D images corrupted by additive white Gaussian\nnoise.\n