Spectral Graph Wavelets and Filter Banks With Low Approximation Error

• Published in: IEEE transactions on signal and information processing over networks 2016-09, Vol.2 (3), p.230-245
• Main Authors: Sakiyama, Akie, Watanabe, Kana, Tanaka, Yuichi
• Format: Article
• Language: English
• Subjects: Chebyshev approximation; Chebyshev polynomial approximation; Discrete cosine transforms; Filter banks; Graph signal processing; Information processing; Spectral analysis; spectral graph filter bank; spectral graph wavelet
• ISSN: 2373-776X; 2373-776X; 2373-7778
• DOI: 10.1109/TSIPN.2016.2581303

We propose filter banks in the graph spectral domain, where each filter is defined by a sum of sinusoidal waves. The main advantages of these filter banks are that (a) they have low approximation errors even if a lower-order shifted Chebyshev polynomial approximation is used, (b) the upper bound of the error after the pth order Chebyshev polynomial approximation can be calculated rigorously without complex calculations, and (c) their parameters can be efficiently obtained from any real-valued linear phase finite impulse response filter banks in regular signal processing. The proposed filter bank has the same filter characteristics as the corresponding classical filter bank in the frequency domain and inherits the original properties, such as tight frame and no DC leakage. Furthermore, their approximation orders can be determined from the desired approximation accuracy. The effectiveness of our approach is evaluated by comparing them with existing spectral graph wavelets and filter banks.