A method for performance analysis of grayscale image denoising techniques based on the wavelet transform

Wavelet transform-based filters are widely adopted for noise removal from grayscale digital images because these techniques can effectively combine cancellation of noise and preservation of image details. The aim of this paper is to provide accurate quantitative evaluations of these key filtering features without the limitations (and the errors) of current metrics. For the first time, the exact amounts of filtering distortion and unfiltered noise produced by a wavelet-based denoising filter are formally computed resorting to the filter theory only. Computer simulations are reported in the paper in order to show how residual noise and filtering distortion affect the results at the pixel level. Comparisons with current metrics are also provided.