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Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/156926

Title:	Increasing resolution and instability for linear inverse scattering problems
Authors:	邱普照 Kow, Pu-Zhao;Salo, Mikko;Zou, Sen
Contributors:	應數系
Keywords:	Linear inverse problems;Instability mechanisms;Increasing stability/resolution;Singular value
Date:	2025-07
Issue Date:	2025-05-09 11:27:28 (UTC+8)
Abstract:	In this work we study the increasing resolution of linear inverse scattering problems at a large fixed frequency. We consider the problem of recovering the density of a Herglotz wave function, and the linearized inverse scattering problem for a potential. It is shown that the number of features that can be stably recovered (stable region) becomes larger as the frequency increases, whereas one has strong instability for the rest of the features (unstable region). To show this rigorously, we prove that the singular values of the forward operator stay roughly constant in the stable region and decay exponentially in the unstable region. The arguments are based on structural properties of the problems and they involve the Courant min-max principle for singular values, quantitative Agmon-Hörmander estimates, and a Schwartz kernel computation based on the coarea formula.
Relation:	Journal of Functional Analysis, Vol.289, No.1, 110923 (37 pages)
Data Type:	article
DOI 連結:	https://doi.org/10.1016/j.jfa.2025.110923
DOI:	10.1016/j.jfa.2025.110923
Appears in Collections:	[應用數學系] 期刊論文

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