Analysis of Framelet Transforms on a Simplex
arXiv:1701.015953 citationsh-index: 16
AI Analysis
This work extends framelet theory to simplex domains, offering a new tool for signal processing on non-standard geometries.
The paper constructs framelets on a simplex and provides fast framelet transforms with exact reconstruction for tight framelets, achieving FFT-like speed.
In this paper, we construct framelets associated with a sequence of quadrature rules on the simplex $T^{2}$ in $\mathbb{R}^{2}$. We give the framelet transforms -- decomposition and reconstruction of the coefficients for framelets of a function on $T^{2}$. We prove that the reconstruction is exact when the framelets are tight. We give an example of construction of framelets and show that the framelet transforms can be computed as fast as FFT.