Removing random-valued impulse noise with reliable weight.

Jin Qiyu (1) , Li Bai (2) , Ion Grama (3) , Quansheng Liu (3) , Yang Jie (4)

1 Inner Mongolia University
2 UON - University of Nottingham, UK
3 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique
4 Shanghai Jiao Tong University [Shanghai]

In this paper, we present a patch based weighted means filter for removing an impulse noise by adapting the fundamental idea of the non-local means filter to the random-valued impulse noise. Our approach is to give a weight to a pixel in order to evaluate the probability that the pixel is contaminated by the impulse noise, which we call Reliable Weight of the pixel. With the help of the Reliable Weights we introduce the similarity function to measure the similarity among patches of the image contaminated by a random impulse noise. It turns out that the similarity function has significant anti impulse noise interference ability. We then incorporate the Reliable Weights and the similarity function into a filter designed to remove the random impulse noise. Under suitable conditions, we establish two convergence theorems to demonstrate that our method is feasible. Simulation results confirm that our filter is competitive compared to recently proposed methods.

Domaines: Probabilités [math.PR]; Théorie de l'information et codage [math.IT]

Jin Qiyu, Li Bai, Ion Grama, Quansheng Liu, Yang Jie. Removing random-valued impulse noise with reliable weight.. Inverse Problems and Imaging , 2020, 14 (2), pp.171-203. ⟨10.3934/ipi.2020009⟩. ⟨hal-02487891⟩