Two denoising SURE-LET methods for complex oversampled subband decompositions

Redundancy in wavelets and filter banks has the potential to greatly improve signal and image denoising. Having developed a framework for optimized oversampled complex lapped transforms, we propose their association with the statistically efficient Stein´s principle in the context of mean square error estimation. Under Gaussian noise assumptions, expectations involving the (unknown) original data are expressed using the observation only. Two forms of Stein´s Unbiased Risk Estimators, derived in the coefficient and the spatial domain respectively, are proposed, the latter being more computationally expensive. These estimators are then employed for denoising with linear combinations of elementary threshold functions. Their performances are compared to the oracle, and addressed with respect to the redundancy. They are finally tested against other denoising algorithms. They prove competitive, yielding especially good results for texture preservation.