The validity analysis of the non-local mean filter and a derived novel denoising method

Image denoising is an important topic in the digital image processing field. This paper theoretically studies the validity of the classical non-local mean filter (NLM) for removing Gaussian noise from a novel statistic perspective. By regarding the restored image as an estimator of the clear image from the statistical view, we gradually analyse the unbiasedness and effectiveness of the restored value obtained by the NLM filter. Then, we propose an improved NLM algorithm called the clustering-based NLM filter (CNLM) that derived from the conditions obtained through the theoretical analysis. The proposed filter attempts to restore an ideal value using the approximately constant intensities obtained by the image clustering process. Here, we adopt a mixed probability model on a prefiltered image to generate an estimator of the ideal clustered components. The experimental results show that our algorithm obtains considerable improvement in peak signal-to-noise ratio (PSNR) values and visual results when removing Gaussian noise. On the other hand, the considerable practical performance of our filter shows that our method is theoretically acceptable as it can effectively estimates ideal images.