Quaternion Mahalanobis Non-local Means for Color Image Denoising

Abstract

By improving the quaternion non-local means (QNLM) image denoising algorithm, the quaternion Mahalanobis non-local means (QMNLM) method is proposed. This method combines quaternion with non-local similarity priors and introduces quaternion Mahalanobis distance. Firstly, the Mahalanobis distance between the image patches is calculated in the eigenspace by singular value decomposition of quaternion since the Mahalanobis distance is not robust in the sample space. Secondly, the image data is analyzed with the principal component analysis method, thus the Mahalanobis distance equation is simplified. The image with noise affected by high noise was first processed with a Gaussian low pass filter (LPF). Experimental results show that the noise reduction effect of this method is better than the non-local means (NLM), generalized non-local Means (GNLM) and QNLM methods. The proposed algorithm can effectively eliminate image noise and efficiently improve the image visual effect.