On the biased estimation of nonlocal means filter

The recent nonlocal means filter (NLM) exhibits exciting performance for image or video denoising. However, the estimation of NLM is biased and tends to keep the value of noise. In the process of NLM, the target pixel (the pixel being processed) is involved in patch distance measuring, which, in turn, controls the restoration of the target pixel. Such design makes the estimation of the target pixel to be biased to the noise. The biased estimation may degrade the reconstruction especially when the noise energy is large. In this paper, the cause and influence of such biased estimation phenomenon is analyzed in detail. We will show that the biased estimation can be extremely harmful or helpful, depending on the degree of noise. Taking advantage of this, a new method is proposed to adaptively control the contribution of target pixel in patch distance measuring. This method achieves much better denoising performance compared with NLM.