Removing Gaussian noise for colour images byquaternion representation and optimisation ofweights in non-local means filter
Résumé
In this study, a new quaternion filter for removal of Gaussian noise in colour images is presented. It is based on thequaternion representation of colour images and the optimisation of a tight bound of the quaternion mean-square error between therestored colour image and the original one, together with the essential idea of the non-local means filter. The optimal weights areobtained by using the method of Lagrange multipliers. The authors’ quaternion optimal weights non-local means filter is given bythe weighted means of the observed quaternion representation using the optimal weights. Experiments on commonly used imagesare provided to illustrate the efficiency of the proposed filter.