Median filter with varying bandwidth adaptive to unknown smoothness of the signal

We describe a novel approach to solve a problem of bandwidth selection for median filtering a signal given with an additive noise. The approach is based on the intersection of confidence intervals ICI rule and gives the algorithm, which is simple to implement and nearly ideal within lnN factor in the point-wise mean squared errors risk for estimating the signal. The ICI rule gives the adaptive varying bandwidths and enables the algorithm to be spatial adaptive in the sense that its quality is close to that which one could achieve if the smoothness of the estimated signal was known in advance