  Non-local self-similarity based low rank algorithms are the state-of-the-art
methods for image denoising. In this paper, a new method is proposed by solving
two issues: how to improve similar patches matching accuracy and build an
appropriate low rank matrix approximation model for Gaussian noise. For the
first issue, similar patches can be found locally or globally. Local patch
matching is to find similar patches in a large neighborhood which can alleviate
noise effect, but the number of patches may be insufficient. Global patch
matching is to determine enough similar patches but the error rate of patch
matching may be higher. Based on this, we first use local patch matching method
to reduce noise and then use Gaussian patch mixture model to achieve global
patch matching. The second issue is that there is no low rank matrix
approximation model to adapt to Gaussian noise. We build a new model according
to the characteristics of Gaussian noise, then prove that there is a globally
optimal solution of the model. By solving the two issues, experimental results
are reported to show that the proposed approach outperforms the
state-of-the-art denoising methods includes several deep learning ones in both
PSNR / SSIM values and visual quality.
