Fuzzy Hysteresis Smoothing: A New Approach for Image Denoising

摘要

Hysteresis smoothing (HS) is one of the recently proposed image denoising schemes, which employs hard threshold levels to model the hysteresis process. Nevertheless, hard thresholding is in contrast with what is observed from the behavior of the hysteresis phenomenon in nature, and this implies that the HS may lead to a suboptimal model. On the other hand, it is proved that fuzzy logic is a promising research field in solving various problems by applying the uncertainty characteristics. Hence, in this article, we develop a novel HS methodology based on the fuzzy norms, which, in addition to incorporating the advantages of the HS, also manages the undesired effects of hard thresholding. In this method, which is called fuzzy HS (FHS), pointwise hard thresholding is replaced by an interval soft manner, which allows the threshold levels to be determined commensurate with the fuzzy norm's free parameter. It is shown that among the classical fuzzy norms, the Yager one can carry out the FHS relatively well. However, this norm causes oversaturation in the hysteresis loop, which leads to an oversmoothing problem in the image denoising process. To alleviate this, a new fuzzy norm with logarithmic nature, named expansion norm, has been proposed, which improves the accuracy of the FHS. The comparative simulations demonstrate the significant superiority of the FHS in terms of both objective and subjective criteria over the classical HS. Besides, the results indicate that the proposed scheme has competitive denoising performance in comparison with some well-known algorithms.