A unified sensitivity kernel for coherent wave tomography in radar, seismic, ultrasound, and optical imaging

Abstract

Imaging an inhomogeneous medium with waves rests on the response of a boundary measurement to a change of the medium inside, formally the sensitivity kernel of the inverse problem. Here we show that the kernels of radar, seismology, medical ultrasound, and diffuse optics all reduce to just two classes. Every kernel is the product of a forward and an adjoint field, and a real measurement retains one quadrature of that product. These quadratures are the two classes, selected either by a component of the material parameter or by the misfit, the structure that persists for the coherent-wave kernel in both the ballistic and the diffusive regime. We place these areas on one diagram of scattering strength and transport depth, exposing a shared computational limit set by wavefield storage, and propose a broadband on-shell compression that can relax that limit.

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BibTeX RIS

BibTeX

@misc{yamilov2026unified,
  title = {{A unified sensitivity kernel for coherent wave tomography in radar, seismic, ultrasound, and optical imaging}},
  author = {Alexey Yamilov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.31583},
  eprint = {2609.31583},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31583},
  note = {CC BY-NC-ND 4.0},
}

RIS

TY  - UNPB
TI  - A unified sensitivity kernel for coherent wave tomography in radar, seismic, ultrasound, and optical imaging
AU  - Alexey Yamilov
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.31583
UR  - https://arxiv.org/abs/2609.31583
AB  - Imaging an inhomogeneous medium with waves rests on the response of a boundary measurement to a change of the medium inside, formally the sensitivity kernel of the inverse problem. Here we show that the kernels of radar, seismology, medical ultrasound, and diffuse optics all reduce to just two classes. Every kernel is the product of a forward and an adjoint field, and a real measurement retains one quadrature of that product. These quadratures are the two classes, selected either by a component of the material parameter or by the misfit, the structure that persists for the coherent-wave kernel in both the ballistic and the diffusive regime. We place these areas on one diagram of scattering strength and transport depth, exposing a shared computational limit set by wavefield storage, and propose a broadband on-shell compression that can relax that limit.
ER  -

Abstract

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