Multidimensional directional filter banks and surfacelets

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 unsolv...

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Veröffentlicht in:IEEE transactions on image processing : a publication of the IEEE Signal Processing Society. - 1992. - 16(2007), 4 vom: 19. Apr., Seite 918-31
1. Verfasser: Lu, Yue M (VerfasserIn)
Weitere Verfasser: Do, Minh N
Format: Aufsatz
Sprache:English
Veröffentlicht: 2007
Zugriff auf das übergeordnete Werk:IEEE transactions on image processing : a publication of the IEEE Signal Processing Society
Schlagworte:Evaluation Study Journal Article Research Support, U.S. Gov't, Non-P.H.S.
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520 |a 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 > or =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 N 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 
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