Non-Local means denoising (NLM) algorithm is a milestone algorithm in the field of image processing. The proposal of NLM has opened up the non-local method which has a deep influence. This paper performed a revisit for NLM from two aspects as follows: 1. To alleviate the high computational complexity problem of NLM, a fast algorithm was constructed, which was based on cross-correlation and fast Fourier transform; 2. NLM always blur structures and textures during the noise removal, especially in the case of strong noise. To solve this problem, an Asymptotic Non-Local Means image denoising algorithm is put forward, which uses the property of noise variance to control the filtering parameters. Numerical experiments illustrate that the fast algorithm is 27 times faster than classical implementation with standard parameter configuration, and the ANLM uniformly outperforms classical NLM, in terms of both PSNR and visual effects. @gh - zhangprofessor