Average Interpolating Wavelets on Point Clouds and Graphs

Details Average Interpolating Wavelets on Point Clouds and Graphs Average Interpolating Wavelets on Point Clouds and Graphs

2011-10-10

arxiv.org/abs/1110.2227v1

Mathematics

Functional Analysis

Scientific paper

We introduce a new wavelet transform suitable for analyzing functions on point clouds and graphs. Our construction is based on a generalization of the average interpolating refinement scheme of Donoho. The most important ingredient of the original scheme that needs to be altered is the choice of the interpolant. Here, we define the interpolant as the minimizer of a smoothness functional, namely a generalization of the Laplacian energy, subject to the averaging constraints. In the continuous setting, we derive a formula for the optimal solution in terms of the poly-harmonic Green's function. The form of this solution is used to motivate our construction in the setting of graphs and point clouds. We highlight the empirical convergence of our refinement scheme and the potential applications of the resulting wavelet transform through experiments on a number of data stets.

Affiliated with

Also associated with

No associations

Rating

Average Interpolating Wavelets on Point Clouds and Graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Average Interpolating Wavelets on Point Clouds and Graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Average Interpolating Wavelets on Point Clouds and Graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-471168