Recovery of the sound speed for the Acoustic wave equation from phaseless measurements (bibtex)

by Joonas Ilmavirta, Alden Waters

Abstract:

We recover the higher order terms for the acoustic wave equation from measurements of the modulus of the solution. The recovery of these coefficients is reduced to a question of stability for inverting a Hamiltonian flow transform, not the geodesic X-ray transform encountered in other inverse boundary problems like the determination of conformal factors. We obtain new stability results for the Hamiltonian flow transform, which allow to recover the higher order terms.

Reference:

Recovery of the sound speed for the Acoustic wave equation from phaseless measurements (Joonas Ilmavirta, Alden Waters), Communications in Mathematical Sciences, volume 16, number 4, pp. 1017–1041, 2018.
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We recover the higher order terms for the acoustic wave equation from measurements of the modulus of the solution. The recovery of these coefficients is reduced to a question of stability for inverting a Hamiltonian flow transform, not the geodesic X-ray transform encountered in other inverse boundary problems like the determination of conformal factors. We obtain new stability results for the Hamiltonian flow transform, which allow to recover the higher order terms.
[arXiv]

Bibtex Entry:

@article{acoustic-hamilton, author = {Joonas Ilmavirta and Alden Waters}, title = {{Recovery of the sound speed for the Acoustic wave equation from phaseless measurements}}, month = mar, year = {2018}, journal = {Communications in Mathematical Sciences}, volume = {16}, number = {4}, pages = {1017--1041}, doi = {10.4310/CMS.2018.v16.n4.a5}, arxiv = {1509.07292}, gsid = {943684576739088803}, url={http://users.jyu.fi/~jojapeil/pub/acoustic-arxiv.pdf}, abstract = {We recover the higher order terms for the acoustic wave equation from measurements of the modulus of the solution. The recovery of these coefficients is reduced to a question of stability for inverting a Hamiltonian flow transform, not the geodesic X-ray transform encountered in other inverse boundary problems like the determination of conformal factors. We obtain new stability results for the Hamiltonian flow transform, which allow to recover the higher order terms.} }

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