Interpolatory Nonlinear and Non-Separable Multi-scale Representation: Application to Image Compression

In this paper, we introduce the notion of nonlinear and non-separable multi-scale representation. We show how it can be derived from nonlinear and non-separable subdivision schemes associated to a non-diagonal dilation matrix. We focus on nonlinear multi-scale decomposition where the dilation matrix is either the quincunx or the hexagonal matrix. We then detail the encoding and decoding algorithm of the representation and, in particular, how the EZW (Embedded Zero-tree Wavelet) algorithm adapts in that context. Numerical experiments on image compression conclude the paper.