Removing Gaussian noise for colour images by quaternion representation and optimisation of weights in non-local means filter

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.