@article {27302,
	title = {Multidimensional Directional Filter Banks and Surfacelets},
	journal = {IEEE Transactions on Image Processing},
	volume = {16},
	number = {4},
	year = {2007},
	pages = {918-931},
	abstract = {In 1992, Bamberger and Smith proposed the directional filter bank (DFB) for an efficient directional decomposition of 2-D signals. Due to the nonseparable nature of the system, extending the DFB to higher dimensions while still retaining its attractive features is a challenging and previously unsolved problem. We propose a new family of filter banks, named NDFB, that can achieve the directional decomposition of arbitrary ￼ N-dimensional (N \&gt;= 2) signals with a simple and efficient tree-structured construction. In 3-D, the ideal passbands of the proposed NDFB are rectangular-based pyramids radiating out from the origin at different orientations and tiling the entire frequency space. The proposed NDFB achieves perfect reconstruction via an iterated filter bank with a redundancy factor of ￼in ￼N-D. The angular resolution of the proposed NDFB can be iteratively refined by invoking more levels of decomposition through a simple expansion rule. By combining the NDFB with a new multiscale pyramid, we propose the surfacelet transform, which can be used to efficiently capture and represent surface-like singularities in multidimensional data.
},
	url = {http://lu.seas.harvard.edu/software/surfbox-matlab-and-c-toolbox-implementing-surfacelet-transform-described-following-pa},
	author = {Lu, Y.M. and M. N. Do}
}
