Optimal fractional fourier filtering for graph signals

Date
2021-05-19
Advisor
Instructor
Source Title
IEEE Transactions on Signal Processing
Print ISSN
1053-587X
Electronic ISSN
1941-0476
Publisher
IEEE
Volume
69
Issue
Pages
2902 - 2912
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
Abstract

Graph signal processing has recently received considerable attention. Several concepts, tools, and applications in signal processing such as filtering, transforming, and sampling have been extended to graph signal processing. One such extension is the optimal filtering problem. The minimum mean-squared error estimate of an original graph signal can be obtained from its distorted and noisy version. However, the best separation of signal and noise, and thus the least error, is not always achieved in the ordinary Fourier domain, but rather a fractional Fourier domain. In this work, the optimal filtering problem for graph signals is extended to fractional Fourier domains, and theoretical analysis and solution of the proposed problem are provided along with computational cost considerations. Numerical results are presented to illustrate the benefits of filtering in fractional Fourier domains.

Course
Other identifiers
Book Title
Keywords
Fractional Fourier transform, Graph signal processing (GSP), Optimal filtering, Wiener filter, Graph Fourier transform (GFT), Signal processing on graphs, Graphs
Citation
Published Version (Please cite this version)