Recovery of attenuation coefficients from phaseless measurements for the Helmholtz equation

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.

Keywords

phase less measurements, Helmholtz equation, Gaussian beams

2010 Mathematics Subject Classification

35R30

Full Text (PDF format)

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

Received 23 August 2016

Accepted 14 January 2018

Published 14 May 2018