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There is a growing realization that modeling wavelet coefficients as statistically independent may be a poor assumption. Thus, this paper investigates two efficient models for wavelet coefficient coupling. Spatial statistics which are Markov (commonly used for textures and other random imagery) do not preserve their Markov properties in the wavelet domain; that is, the wavelet-domain covariance Pw does not have a sparse inverse. The main theme of this work is to investigate the approximation of Pw by hierarchical Markov and non-Markov models.