This paper provides a comprehensive review of image denoising algorithms and introduces a new method called Non Local Means (NL-means). The authors define a general methodology to compare and classify classical image denoising algorithms, focusing on the "method noise," which is the difference between the original image and its denoised version. The NL-means algorithm is proven to be asymptotically optimal under a generic statistical image model. The performance of various methods is evaluated through four criteria: mathematical analysis, perceptual-mathematical analysis, quantitative experimental evaluation, and visualization of method noise on natural images. The paper discusses several local smoothing filters, anisotropic filters, total variation minimization, iterated total variation refinement, neighborhood filters, and frequency domain filters. It also provides detailed mathematical proofs and theoretical results for each method, highlighting their strengths and weaknesses. The NL-means algorithm is highlighted for its ability to preserve structure in digital images, making it a significant contribution to the field of image denoising.This paper provides a comprehensive review of image denoising algorithms and introduces a new method called Non Local Means (NL-means). The authors define a general methodology to compare and classify classical image denoising algorithms, focusing on the "method noise," which is the difference between the original image and its denoised version. The NL-means algorithm is proven to be asymptotically optimal under a generic statistical image model. The performance of various methods is evaluated through four criteria: mathematical analysis, perceptual-mathematical analysis, quantitative experimental evaluation, and visualization of method noise on natural images. The paper discusses several local smoothing filters, anisotropic filters, total variation minimization, iterated total variation refinement, neighborhood filters, and frequency domain filters. It also provides detailed mathematical proofs and theoretical results for each method, highlighting their strengths and weaknesses. The NL-means algorithm is highlighted for its ability to preserve structure in digital images, making it a significant contribution to the field of image denoising.