Perfect Reconstruction Two-Channel Filter Banks on Arbitrary Graphs Based on an Optimization Model
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866909365618868224 |
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| author | You, Junxia Yang, Lihua |
| author_facet | You, Junxia Yang, Lihua |
| contents | In this paper, we propose the construction of critically sampled perfect reconstruction two-channel filterbanks on arbitrary undirected graphs.Inspired by the design of graphQMF proposed in the literature, we propose a general ``spectral folding property'' similar to that of bipartite graphs and provide sufficient conditions for constructing perfect reconstruction filterbanks based on a general graph Fourier basis, which is not the eigenvectors of the Laplacian matrix. To obtain the desired graph Fourier basis, we need to solve a series of quadratic equality constrained quadratic optimization problems (QECQPs) which are known to be non-convex and difficult to solve. We develop an algorithm to obtain the global optimal solution within a pre-specified tolerance. Multi-resolution analysis on real-world data and synthetic data are performed to validate the effectiveness of the proposed filterbanks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_02631 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Perfect Reconstruction Two-Channel Filter Banks on Arbitrary Graphs Based on an Optimization Model You, Junxia Yang, Lihua Signal Processing In this paper, we propose the construction of critically sampled perfect reconstruction two-channel filterbanks on arbitrary undirected graphs.Inspired by the design of graphQMF proposed in the literature, we propose a general ``spectral folding property'' similar to that of bipartite graphs and provide sufficient conditions for constructing perfect reconstruction filterbanks based on a general graph Fourier basis, which is not the eigenvectors of the Laplacian matrix. To obtain the desired graph Fourier basis, we need to solve a series of quadratic equality constrained quadratic optimization problems (QECQPs) which are known to be non-convex and difficult to solve. We develop an algorithm to obtain the global optimal solution within a pre-specified tolerance. Multi-resolution analysis on real-world data and synthetic data are performed to validate the effectiveness of the proposed filterbanks. |
| title | Perfect Reconstruction Two-Channel Filter Banks on Arbitrary Graphs Based on an Optimization Model |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2208.02631 |