Multi-resolution deconvolution

Mirza Karamehmedović; Pierre Maréchal; Martin Sæbye Carøe; Lara Baalbaki

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arXiv · 2512.23342

Multi-resolution deconvolution

Mirza Karamehmedović·Pierre Maréchal·Martin Sæbye Carøe·Lara Baalbaki

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Abstract

We extend the classical deconvolution framework in Rn to the case with a pseudodifferential-like solution operator with a symbol depending on both the base and cotangent variable. Our framework enables deconvolution with spatially varying resolution while maintaining a set global stability, and it additionally allows rather general distributional convolution kernels. We provide consistency, convergence and stability results, as well as convergence rates. Finally, we include numerical examples supporting our results and demonstrating advantages of the generalized framework.

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BibTeX RIS

Mirza Karamehmedović, Pierre Maréchal, Martin Sæbye Carøe, Lara Baalbaki. 2025-12-29. Multi-resolution deconvolution. https://arxiv.org/abs/2512.23342

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