Fuzzy Filters for Noise Reduction: The Case of Gaussian Noise

Noise reduction is a well-known problem in image processing. The reduction of noise in an image sometimes is as a goal itself, and sometimes is considered as a pre-processing step. Besides the classical filters for noise reduction, quite a lot of fuzzy inspired filters have been proposed during the past years. However, it is very difficult to judge the quality of this wide variety of filters. For which noise types are they designed? How do they perform for those noise types? How do they perform compared to each other? Can we select filters that clearly outperform the others? Is there a difference between numerical and visual results? In this paper, we answer these questions for images that are corrupted with Gaussian noise