Redundant Wavelets on Graphs and High Dimensional Data Clouds

TL;DR

This paper introduces a novel redundant wavelet transform for high-dimensional data and graphs that improves denoising performance by reorganizing data points to shorten feature paths, achieving results comparable to BM3D.

Contribution

It presents a new wavelet transform that incorporates data-driven reordering to enhance denoising on complex data structures.

Findings

Achieves denoising results close to BM3D

Effectively reorganizes data points to improve transform efficiency

Applicable to high-dimensional and graph-structured data

Abstract

In this paper, we propose a new redundant wavelet transform applicable to scalar functions defined on high dimensional coordinates, weighted graphs and networks. The proposed transform utilizes the distances between the given data points. We modify the filter-bank decomposition scheme of the redundant wavelet transform by adding in each decomposition level linear operators that reorder the approximation coefficients. These reordering operators are derived by organizing the tree-node features so as to shorten the path that passes through these points. We explore the use of the proposed transform to image denoising, and show that it achieves denoising results that are close to those obtained with the BM3D algorithm.