| Paper: | IMDSP-L2.6 | ||
| Session: | Image and Multidimensional Signal Processing: Theory | ||
| Time: | Wednesday, May 19, 17:10 - 17:30 | ||
| Presentation: | Lecture | ||
| Topic: | Image and Multidimensional Signal Processing: M-D Signal Processing Theory and Methods | ||
| Title: | THE DISCRETE TRIANGLE TRANSFORM | ||
| Authors: | Markus Püschel; Carnegie Mellon University | ||
| Martin Rötteler; University of Waterloo | |||
| Abstract: | We introduce the discrete triangle transform (DTT), a non-separable transform for signal processing on a two-dimensional equispaced triangular grid. The DTT is, in a strict mathematical sense, a generalization of the DCT, type III, to two dimensions, since the DTT is built from Chebyshev polynomials in two variables in the same way as the DCT, type III, is built from Chebyshev polynomials in one variable. We provide boundary conditions, signal extension, and diagonalization properties for the DTT. Finally, we give evidence that the DTT has Cooley-Tukey FFT like algorithms that enable its efficient computation. | ||
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