Denoising of Natural Images Using FREBAS Transformation

摘要

If two algorithms of Fresnel transformation are used with suitable parameters, the expansion of images modeled after multiresolution analysis (FREBAS transformation) is possible. This paper proposes a denoising technique of natural images using FREBAS transformation. Constrained least square filter applying in FREBAS transformed space removes noise superimposed on signals very well, however, that noise with specific patterns might remain on the images when processing images have small SN ratio. In this paper we focus our attention on this noise that exhibits isolationism in FREBAS transformed space and propose a new denoising technique that introduces non-linear noise processing in FREBAS transformed space. It was shown that the noises with specific patterns were favorably removed in simulation experiment. In addition, we applied the proposed technique to natural images which contain noise to and compare the method with other denoising techniques from the viewpoint of SNR improvement, image degradation, remained noises. As a result, the proposed technique could remove noise while controlling image degradation and also obtain significant improvements in the SNR on average. In particular, we confirmed that the proposed technique had excellent denoising performance for images with large variations in amplitude.