Validity of non-local mean filter and novel denoising method

Abstract

BackgroundImage denoising is an important topic in the digital image processing field. This study theoretically investigates the validity of the classical nonlocal mean filter (NLM) for removing Gaussian noise from a novel statistical perspective. MethodBy considering the restored image as an estimator of the clear image from a statistical perspective, we gradually analyze the unbiasedness and effectiveness of the restored value obtained by the NLM filter. Subsequently, we propose an improved NLM algorithm called the clustering-based NLM filter that is 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. In this study, we adopt a mixed probability model on a prefiltered image to generate an estimator of the ideal clustered components. ResultThe experiment yields improved peak signal-to-noise ratio values and visual results upon the removal of Gaussian noise. ConclusionHowever, the considerable practical performance of our filter demonstrates that our method is theoretically acceptable as it can effectively estimate ideal images.