| 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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