Adaptive Window Size Image De-noising Based on Intersection of Confidence Intervals (ICI) Rule

We describe a novel approach to solve a problem of window size (bandwidth) selection for filtering an image signal given with a noise. The approach is based on the intersection of confidence intervals (ICI) rule and gives the algorithm, which is simple to implement and nearly optimal in the point-wise mean squared error risk. The local polynomial approximation (LPA) is used in order to derive the 2D transforms (filters) and demonstrate the efficiency of the approach. The ICI rule gives the adaptive varying window size and enables the algorithm to be spatially 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. Optimization of the threshold (design parameter of the ICI) is studied. It is shown that the cross-validation adjustment of the threshold significantly improves the algorithm accuracy. In particular, simulation demonstrates that the adaptive transforms with the adjusted threshold parameter perform better than the adaptive wavelet estimators.