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arXiv · 2402.07093

Stability of the \`A Trous Algorithm Under Iteration

Brody Johnson·Simon McCreary-Ellis
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Abstract

This paper examines the stability of the \`a 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.

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Brody Johnson, Simon McCreary-Ellis. 2024-02-11. Stability of the \`A Trous Algorithm Under Iteration. https://arxiv.org/abs/2402.07093

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