Convergence Theorems For The Non-Local Means Filter - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Inverse Problems and Imaging Année : 2018

Convergence Theorems For The Non-Local Means Filter

Qiyu Jin
Ion Grama

Résumé

We introduce an oracle filter for removing the Gaussian noise with weights depending on a similarity function. The usual Non-Local Means filter is obtained from this oracle filter by substituting the similarity function by an estimator based on similarity patches. When the sizes of the search window are chosen appropriately, it is shown that the oracle filter converges with the optimal rate. The same optimal convergence rate is preserved when the similarity function has suitable errors-in measurements. We also provide a statistical estimator of the similarity which converges at a convenient rate. Based on our convergence theorems, we propose some simple formulas for the choice of the parameters. Simulation results show that our choice of parameters improves the restoration quality of the filter compared with the usual choice of parameters in the original algorithm.

Dates et versions

hal-02019079 , version 1 (14-02-2019)

Identifiants

Citer

Qiyu Jin, Ion Grama, Quansheng Liu. Convergence Theorems For The Non-Local Means Filter. Inverse Problems and Imaging , 2018, 12 (4), pp.853-881. ⟨10.3934/ipi.2018036⟩. ⟨hal-02019079⟩
60 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More