Quaternion Quasi-Chebyshev Non-local Means for Color Image Denoising

Quaternion non-local means (QNLM) denoising algorithm makes full use of high degree self-similarities inside images to suppress the noise, so the similarity metric plays a key role in its denoising performance. In this study, two improvements have been made for the QNLM: 1) For low level noise, the use of quaternion quasi-Chebyshev distance is proposed to measure the similarity of image patches and it has been used to replace the Euclidean distance in the QNLM algorithm. Since the quasi-Chebyshev distance measures the maximal distance in all color channels, the similarity of color images measured by quasi-Chebyshev distance can capture the structural similarity uniformly for each color channel; 2) For high level noise, quaternion bilateral filtering has been proposed as the preprocessing step in the QNLM algorithm. Denoising simulations were performed on 110 images of landscape, people, and architecture at different noise levels. Compared with QNLM, quaternion non-local total variation (QNLTV), and non-local means (NLM) variants (NLTV, NLM after wavelet threshold preprocessing, and the color adaptation of NLM), our novel algorithm not only improved PSNR/SSIM (peak signal to noise rate/structural similarity) and figure of merit values by an average of 2.77 dB/8.96% and 0.0491 respectively, but also reduced processing time.