Correlated non-linear wavelet shrinkage

This paper examines non-linear shrinkage methods specifically taking into account the correlation structure of the multiresolution wavelet coefficients. In contrast to hidden Markov trees, which model the relationship of wavelet variance from scale to scale, here we wish to take advantage of coefficient correlation. A linear shrinkage based on the LLS (Linear Least Square) estimator, employing a sample correlation scheme, is tested and verified to have an aesthetic denoising performance. Then, state-of-the-art independent shrinkage functions are applied to exploit the efficiency of such techniques and to introduce non-linearity into the algorithm to compensate for non-Gaussianity of the wavelet statistics. The performance of the non-linear shrinkage technique, as used individually and together with the linear correlated approach, are illustrated.