Image Denoising Using Non-local Means Filter Based On The Similarity Measurement In The Wavelet Domain

Image denoising has been occupied an important position in image processing field. Its main purpose is to solve the problem of the decline in image quality caused by noise. In recent years, all kinds of image denoising algorithm have been proposed, the Nonlocal means algorithm (NL_means), one of them, has earned a wide attention from people of all walks of life due to its excellent denoising effect and simple algorithm thought while BM3D algorithm, KSVD algorithm and the Nonlocal sparse model let us access to the concept of joint filtering that the filtering process can be composed of a variety of filtering algorithm together. We find that the results of the first filtering have made a very significant effect on the final results of the filtering process through a lot of experiments. Based on the wavelet theory and combined with the Nonlocal means thought, this paper constructs a similarity measurement model based on the noise analysis after wavelet transform for block matching and propose a low frequency similarity measurement distance formula and a high frequency similarity measure distance formula.(1) A similarity measurement model based on Wavelet transform is derived, which give a systemic analysis of noise on the subbands of the noisy image after wavelet transform and a new similarity measurement method is proposed according to the distribution of Euclidean distance between patches got from the subbands of the noisy image after wavelet transform. A lot of experiments have been made proved that the model can better meet the distribution in theory.(2) A Bayesian filtering method based on the wavelet coefficients in low frequency domain is proposed. This method uses the wavelet coefficients in low frequency domain to describe the similarity weights in Bayesian denoising model and devise a low frequency similarity measurement formula which reduce the influences caused by noise in the calculation of similarity weights and improve the accuracy of the similarity weights. The low frequency similarity weights is decided by the distribution of low-frequency coefficients of the image itself, so it requires less parameters. Experimental results are given for the demonstration that compared with the traditional denoising algorithm; this method gets the better effect both in PSNR and the vision.(3) A nonlocal means filtering method based on wavelet coefficients in the high frequency is proposed. Combined with the local mean thought, this method gives a detail analysis of the distribution of the Euclidean distance in all directions of the each scale of the wavelet subband and constructs the corresponding distribution model. Through calculating the numbers of the large coefficients of the image patch in all directions of the each scale of the wavelet subbands, each subband is well combined to describe the similarity of the image patches. Experiments show that the algorithm has better denoising effect, which proves that the establishment of a accurate model of image denoising is significant.This work was supported by the National Natural Science Foundation of China(No.61072106), the Program for Cheung Kong Scholars and Innovative Research Team in University(No.IRT0645)and the Fundamental Research Funds for the Central Universities(No.JY10000902032) for their support.