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arXiv · 2603.21124

Removing small wavenumber constraints in Side B of the Probe Method

Masaru Ikehata
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Abstract

The Probe Method is an analytical reconstruction scheme for inverse obstacle problems utilizing the Dirichlet-to-Neumann map associated with the governing partial differential equation. It consists of two distinct parts: Side A and Side B. Both are based on the indicator sequence which is calculated from the Dirichlet-to-Neumann map acting on "needle-like" specialized solution of the governing equation for the background medium, whose energy is concentrated on an arbitrary given needle inside. In Side A, the limit of the indicator sequence-referred to as the indicator function-is computed before the needles touch the obstacle, and the boundary is identified as the point where this function first blows up. In contrast, Side B states the blow-up of the indicator sequence after the needles have come into contact with the obstacle. For the Helmholtz equation, the validity of Side B has long required a small wavenumber constraint. This paper finally removes this long-standing restriction, establishing the method's applicability for broader cases.

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Masaru Ikehata. 2026-09-10. Removing small wavenumber constraints in Side B of the Probe Method. https://arxiv.org/abs/2603.21124

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