Design of Wavelet Filter Banks for Any Dilation Using Extended Laplacian Pyramid Matrices
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910836326400000 |
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| author | Hur, Youngmi Kim, Sungjoo |
| author_facet | Hur, Youngmi Kim, Sungjoo |
| contents | In this paper, we present a new method for designing wavelet filter banks for any dilation matrices and in any dimension. Our approach utilizes extended Laplacian pyramid matrices to achieve this flexibility. By generalizing recent tight wavelet frame construction methods based on the sum of squares representation, we introduce the sum of vanishing products (SVP) condition, which is significantly easier to satisfy. These flexible design methods rely on our main results, which establish the equivalence between the SVP and mixed unitary extension principle conditions. Additionally, we provide illustrative examples to showcase our main findings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_14242 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Design of Wavelet Filter Banks for Any Dilation Using Extended Laplacian Pyramid Matrices Hur, Youngmi Kim, Sungjoo Information Theory 42C40, 42C15 In this paper, we present a new method for designing wavelet filter banks for any dilation matrices and in any dimension. Our approach utilizes extended Laplacian pyramid matrices to achieve this flexibility. By generalizing recent tight wavelet frame construction methods based on the sum of squares representation, we introduce the sum of vanishing products (SVP) condition, which is significantly easier to satisfy. These flexible design methods rely on our main results, which establish the equivalence between the SVP and mixed unitary extension principle conditions. Additionally, we provide illustrative examples to showcase our main findings. |
| title | Design of Wavelet Filter Banks for Any Dilation Using Extended Laplacian Pyramid Matrices |
| topic | Information Theory 42C40, 42C15 |
| url | https://arxiv.org/abs/2409.14242 |