Iterative alternating optimization of bi-orthogonal two-channel graph filter bank

• Published in: Multidimensional systems and signal processing Vol. 34; no. 2; pp. 447 - 478
• Main Authors: Wang, Hao, Ou, Yi, Cheng, Xinmin, Li, Guangqiu, Ye, Xueyi, Huang, Chengwei
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2023; Springer Nature B.V
• Subjects: Algorithms; Artificial Intelligence; Circuits and Systems; Coefficients; Computational geometry; Convex analysis; Convexity; Design optimization; Electrical Engineering; Engineering; Errors; Filter banks; Optimization; Reconstruction; Signal,Image and Speech Processing; Two-channel; Bi-orthogonal graph filter bank; Iterative alternating optimization; Graph signal processing
• ISSN: 0923-6082; 1573-0824
• DOI: 10.1007/s11045-023-00868-w

The iterative alternating optimization (IAO) algorithm is proposed to optimize the coefficients of the (frequency domain/ spectral) general design two-channel bi-orthogonal graph filter banks (2c-BiO-graph-FB). Its basic idea is iteratively and alternatingly optimizing part of the coefficients while fixing the other coefficients as constants. By utilizing this scheme, the original non-convex optimization design problem is transformed into a series of convex optimization problems. Simulation experiment is conducted to verify the proposed algorithm. The results reveal that the proposed design is an effective one if the order of the graph filter is low. For the low order case, the proposed design can have the smallest frequency selectivity error while simultaneously having exceedingly small reconstruction error ( ≤ 10 - 11 ). Additionally, as a kind of optimization algorithm, it outperforms the existing trust-region-iterative-gradient-searching (TR-IGS) in terms of the reconstruction error and/or the frequency selectivity error. Further, it can also be utilized to effectively optimize the frequency selectivity of two kinds of special design 2c-BiO-graph-FBs which inherently have exceedingly small reconstruction error. Finally, the designed 2c-BiO-graph-FB by the proposed algorithm is applied to two different specific graphs to decompose and synthesize the corresponding graph signals.