$M$-Channel Critically Sampled Spectral Graph Filter Banks With Symmetric Structure

Abstract

This paper proposes a class of M -channel spectral graph filter banks with a symmetric structure, that is, the transform has sampling operations and spectral graph filters on both the analysis and synthesis sides. The filter banks achieve maximum decimation, perfect recovery, and orthogonality. Conventional spectral graph transforms with decimation have significant limitations with regard to the number of channels, the structures of the underlying graph, and their filter design. The proposed transform uses sampling in the graph frequency domain. This enables us to use any variation operators and apply the transforms to arbitrary graphs even when the filter banks have symmetric structures. We clarify the perfect reconstruction conditions and show design examples. An experiment on graph signal denoising conducted to examine the performance of the proposed filter bank is described.

Sparse-Coded Dynamic Mode Decomposition on Graph for Prediction of River Water Level Distribution

“…Graph signal processing (GSP) is a signal processing based on the analysis of graph spectral characteristics of signals with a definition range on graph vertices [17][18][19][20]. If graph structure is known, GSP provides us an efficient means of storage, transmission and analysis for signals on the graph.…”

“…In this paper, we propose a novel river water level prediction model based on the graph structure of a river, employing a graph filter bank (GFB) as a convolutional dictionary in CSC-DMD [17][18][19][20]. GFBs are analysis and synthesis systems for graph signals, which are signals defined on graph vertices, and are applied to approximation, restoration and prediction of signals on graphs.…”

A Modified Spline Graph Filter Bank

“…This is a big challenge for multiscale analysis and processing on arbitrary graphs. To deal with this challenge, different approaches have emerged, [18]- [21]. The authors in [18] and [19] proposed a GFB structure without down/upsampling that leads to a large computational load.…”

“…The authors in [18] and [19] proposed a GFB structure without down/upsampling that leads to a large computational load. In contrast, the authors in [20] and [21], take a more interesting approach and perform down/upsampling operations in spectral domain. This idea led to a critically-sampled GFB structure with spectral sampling (GraphSS) that is applicable to arbitrary graphs while satisfying the PR condition.…”

“…This idea led to a critically-sampled GFB structure with spectral sampling (GraphSS) that is applicable to arbitrary graphs while satisfying the PR condition. The concept of spectral sampling, its superior performance to vertex domain methods, [16], and the results of [20] and [21] are among the main motivations for extending SGFB, [15], from vertex domain to spectral domain in this paper. In [15], the designed analysis filters do not have desirable passband/stop-band characteristics.…”