The inefficiency of separable wavelets in representing smooth edges has motivated the researchers to pursue new two dimensional transformations. One of the successful transformations in image compression is the directional wavelets. Although researchers have empirically shown that the directional wavelets outperform the separable wavelets in compression, there is no theoretical analysis to demonstrate this phenomena, specially when the directional wavelets are combined with partitioning algorithms such as quadtree. In this paper, we calculate the rate-distortion performance of the directional wavelets on a class of images. Our analysis shows that the quadtree partitioning deteriorates the performance. Therefore we propose another scheme, called megablocking. Our theoretical and simulation results confirm that megablocking outperforms the quadtree approach.

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