Indeed, the GGD modeling in wavelet subbands is closely related to the ability of (some) wavelets to sparsily represent (some) images with few important coefficients. I am collecting (and would share when ready) some references regarding such generalized gaussian models with dual-tree complex, contourlets, curvelets, shearlets, and other types of directional, multiscale transforms. As of today, i do not know of a paper comparing these transforms in terms of modeling.
The Dual Tree Complex Wavelet Transform has complex coefficients for which is possible better to use a complex repartition as for example a Complex Generalized Gaussian Distribution:
M. Novey, T. Adali, and A. Roy, “A complex generalized Gaussian distribution-Characterization, generation, and estimation”, IEEE Trans. Signal Processing, vol. 58, no. 3, part. 1, pp. 1427-1433, March 2010.
Besides GGD, wavelet coefficients can also be effectively modeled by Gaussian Mixture Model (GSM). Using GSM with Hidden Markov Tree model, we have a tool to investigate statistical relations such as inter-band, intra-band correlation, etc. Google scholar for the term Wavelet Hidden Markov Model will lead you to several relating publications. Hope those information helps for researchers who have similar questions in mind.
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