Pixel-level Non-local Self-similarity in Quaternion-encoded Color Image Denoising

Low-rank quaternion recovery (LRQR) can effectively utilize the correlation between the RGB channels in color image denoising. However, the underlying low-rank structure of image relies on the patch-level non-local self-similarity (NSS), whose accuracy needs to be further improved. In our paper, we propose a pixel-level NSS method based on the patch-level NSS to more accurately capture the underlying low-rank structure of quaternion-encoded color image. Specifically, we propose a row matching method that performs fine screening on the basis of patch-level similar groups to obtain pixel-level similar groups, and then perform $\operatorname{LRQR}$ on them based on the Laplace function. We also propose a weighted aggregation method to measure the contribution of recovery effects of different groups. Experiments on synthetic noise images and real noise images show that when the noise variance is 10, 30, and 50, our proposed method increases at least $0.32 \mathrm{~dB}, 0.62 \mathrm{~dB}$, and 0.58 dB on the average of PSNR, respectively.