The Discrete Cosine Transform on Triangles

The discrete cosine transform is a valuable tool in analysis of data on undirected rectangular grids, like images. In this paper it is shown how one can define an analogue of the discrete cosine transform on triangles. This is done by combining algebraic signal processing theory with a specific kind...

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Bibliographic Details
Main Authors: Seifert, Bastian, Huper, Knut
Format: Conference Proceeding
Language:English
Subjects:
Algebra
algebraic signal processing
Chebyshev approximation
Christoffel-Darboux formula
discret cosine transform
Discrete cosine transforms
lattice of triangles
Lattices
multivariate Chebyshev polynomials
Signal processing
Surface treatment
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Summary:The discrete cosine transform is a valuable tool in analysis of data on undirected rectangular grids, like images. In this paper it is shown how one can define an analogue of the discrete cosine transform on triangles. This is done by combining algebraic signal processing theory with a specific kind of multivariate Chebyshev polynomials. Using a multivariate Christoffel-Darboux formula it is shown how to derive an orthogonal version of the transform.
ISSN:2379-190X
DOI:10.1109/ICASSP.2019.8682222