Atomic approximation allows us to link wavelet coefficients at different scale levels. We have seen that their exact evolution law can be then provided along with their trajectories through scales.This can be exploited for signal and image compression. In fact, the knowledge of how information propagates across scales as well as the link between wavelet low pass component and atoms allow us to effectively compact information. As a result, the decoder only receives the coarsest low pass band. From this it is possible to estimate the atomic representation of wavelet details and then recover an approximation of the original signal. The coarsest low pass band is encoded via a DCT retaining and quantizing just a few coefficients. Experimental results show that the proposed model is able to outperform the existing compression schemes in terms of both rate and distortion with a low computational effort [1].
However, in the approach above the computational burden due to the DCT may be avoided by suitably and non uniformly sampling the coarsest low pass band. An optimal sampling based on the minimax is in [2].
References: