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| Paper: | SS-10.5 |
| Session: | Manifolds and Geometry in Signal Processing |
| Time: | Friday, May 21, 10:50 - 11:10 |
| Presentation: |
Special Session Lecture |
| Topic: |
Special Sessions: Manifolds and Geometry in Signal Processing |
| Title: |
DIRECTIONAL HYPERCOMPLEX WAVELETS FOR MULTIDIMENSIONAL SIGNAL ANALYSIS AND PROCESSING |
| Authors: |
Wai Lam Chan; Rice University | | |
| | Hyeokho Choi; Rice University | | |
| | Richard Baraniuk; Rice University | | |
| Abstract: |
We extend the wavelet transform to handle multidimensional signals that are smooth save for singularities along lower-dimensional manifolds. We first generalize the complex wavelet transform to higher dimensions using a multidimensional Hilbert transform. Then, using the resulting hypercomplex wavelet transform (HWT) as a building block, we construct new classes of nearly shift-invariant wavelet frames that are oriented along lower-dimensional subspaces. The HWT can be computed efficiently using a 1-D dual-tree complex wavelet transform along each signal axis. We demonstrate how the HWT can be used for fast line detection in 3-D. |
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