Sparse image representation through multiple multiresolution analysis

We present a strategy for image data sparsification based on a multiple multiresolution representation obtained through a structured tree of filterbanks, where both the filters and decimation matrices may vary with the decomposition level. As an extension of standard wavelet and wavelet-like approaches, our method also captures directional anisotropic information of the image while maintaining a controlled implementation complexity due to its filterbank structure and to the possibility of expressing the employed 2-D filters in an almost separable aspect. The focus of this work is on the transformation stage of image compression, emphasizing the sparsification of the transformed data. The proposed algorithm exploits the redundancy of the transformed image by applying an efficient sparse selection strategy, retaining a minimal yet representative subset of coefficients while preserving most of the energy of the data.