A fuzzy approach to performance measurement of grayscale image denoising algorithms

The most advanced metrics for performance evaluation of image denoising algorithms are based on the classification of filtered pixels in two crisp classes: pixels where residual noise is still present (due to insufficient filtering) and pixels where excessive filtering has produced distortion. However, the intrinsic nature of image denoising is very likely to be fuzzy: a pixel can be affected by different degrees of unfiltered noise and filtering distortion as well. According to this idea, a new method for performance measurement of grayscale image denoising filter is presented. The method adopts a fuzzy model-based procedure that estimates, for each filtered pixel, the different components of the filtering error, i.e., the amounts of unfiltered noise and filtering distortion produced by the denoising process. Computer simulations dealing with different test images corrupted by various amounts of noise show that the new approach performs significantly better than state-of-the art metrics in the field. Furthermore, the results yielded by the proposed method are in perfect agreement with the true values of residual noise and image blur that can be theoretically evaluated for an important class of denoising filters.