Stability of the À Trous Algorithm Under Iteration
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916121602424832 |
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| author | Johnson, Brody McCreary-Ellis, Simon |
| author_facet | Johnson, Brody McCreary-Ellis, Simon |
| contents | This paper examines the stability of the à trous algorithm under arbitrary iteration in the context of a more general study of shift-invariant filter banks. The main results describe sufficient conditions on the associated filters under which an infinitely iterated shift-invariant filter bank is stable. Moreover, it is shown that the stability of an infinitely iterated shift-invariant filter bank guarantees that of any associated finitely iterated shift-invariant filter bank, with uniform bounds. The reverse implication is shown to hold under an additional assumption on the low-pass filter. Finally, it is also shown that the separable product of stable one-dimensional shift-invariant filter banks produces a stable two-dimensional shift-invariant filter bank. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07093 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of the À Trous Algorithm Under Iteration Johnson, Brody McCreary-Ellis, Simon Classical Analysis and ODEs 42C15, 94A12 This paper examines the stability of the à trous algorithm under arbitrary iteration in the context of a more general study of shift-invariant filter banks. The main results describe sufficient conditions on the associated filters under which an infinitely iterated shift-invariant filter bank is stable. Moreover, it is shown that the stability of an infinitely iterated shift-invariant filter bank guarantees that of any associated finitely iterated shift-invariant filter bank, with uniform bounds. The reverse implication is shown to hold under an additional assumption on the low-pass filter. Finally, it is also shown that the separable product of stable one-dimensional shift-invariant filter banks produces a stable two-dimensional shift-invariant filter bank. |
| title | Stability of the À Trous Algorithm Under Iteration |
| topic | Classical Analysis and ODEs 42C15, 94A12 |
| url | https://arxiv.org/abs/2402.07093 |