Communications in Mathematical Sciences

Volume 16 (2018)

Number 2

Recovery of attenuation coefficients from phaseless measurements for the Helmholtz equation

Pages: 579 – 587

(Fast Communication)



Alden Waters (Johann Bernoulli Instituut, Rijksuniversiteit Groningen, The Netherlands)


We consider the Helmholtz equation with a complex attenuation coefficient on a bounded, strictly convex domain in $\mathbb{R}^d$. We prove a Hölder conditional stability estimate for identifying attenuation coefficients from phaseless boundary value measurements, when the initial excitation state is in the form of a Gaussian bump. We use the Gaussian beam Ansatz and stability results for the X-ray transform on strictly convex domains to establish these estimates.


phase less measurements, Helmholtz equation, Gaussian beams

2010 Mathematics Subject Classification


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A. W. acknowledges support by EPSRC grant EP/L01937X/1.

Received 23 August 2016

Accepted 14 January 2018

Published 14 May 2018