Redundant multiscale transforms and their application for morphological component separation

The development track of the wavelet transform and its redundant extensions designed for images was described. The notion of sparsity and the algorithms that facilitate it was studied. It was found that the combination of multiscale transforms leads to a powerful method in the morphological component analysis (MCA) framework. The results show that a very high-quality restoration can be achieved in an efficient way using several multiscale transforms without having to perform a full decomposition of the original image.