Chan, Wai LamChoi, HyeokhoBaraniuk, Richard G.2007-10-312007-10-312004-05-012004-05-01W. L. Chan, H. Choi and R. G. Baraniuk, "Directional Hypercomplex Wavelets for Multidimensional Signal Analysis and Processing," vol. 3, 2004.https://hdl.handle.net/1911/19796Conference PaperWe 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 <i>hypercomplex wavelet transform</i> (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.engmultidimensional wavelet transformHilbert transformhypercomplexquaternionsWavelet based Signal/Image ProcessingConference papermultidimensional wavelet transformHilbert transformhypercomplexquaternionshttp://dx.doi.org/10.1109/ICASSP.2004.1326715