Open AccessRemoving Gaussian noise for colour images by quaternion representation and optimisation of weights in non‐local means filter
Author(s) -
Chen Beijing,
Liu Quansheng,
Sun Xingming,
Li Xu,
Shu Huazhong
Publication year - 2014
Publication title -
iet image processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.401
H-Index - 45
eISSN - 1751-9667
pISSN - 1751-9659
DOI - 10.1049/iet-ipr.2013.0521
Subject(s) - quaternion , noise (video) , representation (politics) , gaussian noise , filter (signal processing) , gaussian , artificial intelligence , computer science , gaussian filter , computer vision , mathematics , algorithm , pattern recognition (psychology) , image (mathematics) , physics , geometry , quantum mechanics , politics , political science , law
In this study, a new quaternion filter for removal of Gaussian noise in colour images is presented. It is based on the quaternion representation of colour images and the optimisation of a tight bound of the quaternion mean‐square error between the restored colour image and the original one, together with the essential idea of the non‐local means filter. The optimal weights are obtained by using the method of Lagrange multipliers. The authors' quaternion optimal weights non‐local means filter is given by the weighted means of the observed quaternion representation using the optimal weights. Experiments on commonly used images are provided to illustrate the efficiency of the proposed filter.