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\begin{document}

\title{Tomography across scales: Knowledge transfer from seismology to imaging
breast tissue with ultrasound}



\author[1]{Naiara Korta Martiartu}%
\author[1]{Christian Boehm}%
\author[1]{Vaclav Hapla}%
\author[1]{Andreas Fichtner}%
\affil[1]{ETH Zurich}%


\vspace{-1em}



  
  \date{May 24, 2024}


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\begin{abstract}
Ultrasound Computer Tomography (USCT) is an emerging technique for
breast cancer screening. Ultrasonic waves are propagated through the
tissue and recorded by a set of transducers that are surrounding the
breast. The experiment collects transmission and reflection data, which
are used to obtain quantitative images of acoustic properties of the
tissue (see Figure). This information is useful to characterize the
breast tissue, and improves the specificity of standard imaging
modalities. However, providing a diagnostic tool with high accuracy and
clinically affordable time-to-solution (goal: \textasciitilde{}15
min/patient) still remains a challenge. The goal of this work is to show
that, despite the vast scale differences, experiments in seismology and
USCT share many similarities. In both fields, the relative wave speed
variations are comparable and the number of propagated wavelengths in
the domain has the same order of magnitude. Because the wave equation is
scale invariant, the cross-fertilization between both fields will
benefit imaging methods on all scales. In this study, we present methods
from seismic tomography that we have recently introduced to USCT: 1) We
employ a linearized finite-frequency traveltime tomography approach for
speed-of-sound reconstruction. Using the cross-correlation traveltime
misfit functional, we compute analytically the sensitivity kernels using
adjoint techniques. Our method can operate almost in real time while
still including finite-frequency effects. It also can retrieve useful 3D
information from 2D acquisition systems. 2) Similar to exploration
geophysics, both speed-of-sound and reflectivity images are important
for the interpretation. Here, we suggest a framework that combines
full-waveform inversion for speed-of-sound and reverse time migration
for reflectivity. 3) We apply the Sequential Optimal Experimental Design
(SOED) method to optimize the position and number of transducers, in
terms of accuracy and cost, to image both reflection and transmission
information. Using the Bayesian approach, we define the quality of a
design as the average of the posterior variances of the parameters. SOED
provides cost-benefit curves that quantifies the information gain versus
the computational cost. These are useful to control the trade-off
between accuracy and practicality.%
\end{abstract}%



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