Data Adaptive Median Filters for Signal and Image Denoising Using a Generalized SURE Criterion

Due to its effectiveness for removing heavy-tail noise and preserving abrupt structures hidden in noisy data, median filtering has long been a popular tool for signal restoration. In practice, an important issue of applying median filtering is the choice of the span. In this letter, we develop a data adaptive criterion for choosing this span. This criterion is derived using the generalized SURE technique recently proposed by Shen and Huang. It is designed to handle outliers and heavy-tail noise, and it aims to minimize the mean-squared error between the true and restored signals. Results from simulation experiments suggest that the proposed criterion is superior to its competitors