Spectral graph wavelet packets frames

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Applied and Computational Harmonic Analysis Pub Date : 2023-09-01 DOI:10.1016/j.acha.2023.04.003

Iulia Martina Bulai , Sandra Saliani

引用次数: 0

Abstract

Classical wavelet, wavelet packets and time-frequency dictionaries have been generalized to the graph setting, the main goal being to obtain atoms which are jointly localized both in the vertex and the graph spectral domain. We present a new method to generate a whole dictionary of frames of wavelet packets defined in the graph spectral domain to represent signals on weighted graphs.

We will give some concrete examples on how the spectral graph wavelet packets can be used for compressing, denoising and reconstruction by considering a signal, given by the fRMI (functional magnetic resonance imaging) data, on the nodes of voxel-wise brain graph with 900760 nodes, representing the brain voxels.

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谱图小波包帧

经典的小波、小波包和时频字典已被推广到图设置中，主要目标是获得在顶点和图谱域中联合定位的原子。我们提出了一种新的方法来生成在图谱域中定义的小波包帧的完整字典，以表示加权图上的信号。我们将给出一些具体的例子，说明如何通过考虑由fRMI（功能磁共振成像）数据在具有900760个节点的体素脑图节点上给出的信号，将频谱图小波包用于压缩、去噪和重建，表示脑体素。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied and Computational Harmonic Analysis 物理-物理：数学物理

CiteScore

5.40

自引率

4.00%

发文量

审稿时长

22.9 weeks

期刊介绍： Applied and Computational Harmonic Analysis (ACHA) is an interdisciplinary journal that publishes high-quality papers in all areas of mathematical sciences related to the applied and computational aspects of harmonic analysis, with special emphasis on innovative theoretical development, methods, and algorithms, for information processing, manipulation, understanding, and so forth. The objectives of the journal are to chronicle the important publications in the rapidly growing field of data representation and analysis, to stimulate research in relevant interdisciplinary areas, and to provide a common link among mathematical, physical, and life scientists, as well as engineers.