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Novel class-based entropy coding algorithms for lattice quantised hierarchical (or interband) vectors are presented. The vectors are formed from wavelet coefficients on different scales from similarly oriented sub-bands corresponding to the same spatial location. Structures have been designed specifically for interband vectors drawn from wavelet coefficients, where large groups of approximately equiprobable lattice points are grouped into relatively few classes, known as sub-classes, super-classes and super-super-classes, enabling accurate probability estimates from training data to be obtained for entropy coding of the class indices. Further, it has been found that the best quantiser is a combination of the Zn, and Dn lattices which has been termed an augmented lattice. The performance of the method, entitled entropy-coded pyramid vector quantisation (ECPVQ), is evaluated on real images and the results show that ECPVQ is competitive, particularly at low bit-rates, with current state-of-the-art wavelet-based coders. A subjective comparison with current high performance scalar quantisation based coders shows that ECPVQ is likely to better preserve fine texture detail in the decoded images because of the finer quantisation of low energy wavelet coefficients that occurs with the augmented lattice