Optimal SURE parameters for sigmoidal wavelet shrinkage

This paper provides a SURE optimization for the parameters of a sub-class of smooth sigmoid based shrinkage functions. The optimization is performed on an unbiased estimation risk obtained by using sigmoid shrinkage functions. The SURE sigmoid shrinkage performance measurements are compared to those of the SURELET (SURE linear expansion of thresholds) parameterization. It is shown that the SURE sigmoid shrinkage performs better than the SURELET parameterization on most standard images. The relevance of SigShrink is reinforced by the flexible spatial adaptation it provides thanks to its parameters: a threshold for discriminating large and small data and an attenuation degree to control the shrinkage imposed to data with small amplitudes.