Using optimal transport to mitigate cycle-skipping in ultrasound computed tomography

Boehm, Christian; Krischer, Lion; Ulrich, Ines Elisa; Marty, Patrick; Afanasiev, Michael; Fichtner, Andreas

doi:10.1117/12.2605894

Cited by 9 publications

(8 citation statements)

References 17 publications

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“…This also suggests that all starting models are in the locally convex region of the misfit functional, which also justifies the use of uncertainty quantification using a Gaussian approximation and information derived from the Hessian (Bui‐Thanh et al., 2013). The minimal effect of the starting model also means that starting with a one‐dimensional starting model (e.g., Boehm et al., 2022; Métivier et al., 2016) is not required to minimize artifacts of the starting model in areas with dense ray coverage. 1D starting models require significantly more iterations due to the layered structure and lack of lateral heterogeneity; using a 3D starting model will minimize computational time while still not contributing artifacts.…”

Section: Discussionmentioning

confidence: 99%

“…In past studies, models are often presented as updates of previous models, using the last version of the model as the starting model for the current model (e.g., Bozdag et al., 2016; French et al., 2013; French & Romanowicz, 2014; Lei et al., 2020). Recent studies have also begun to use 1‐D velocity models such as the Preliminary Reference Earth Model (PREM; Dziewonski & Anderson, 1981) to avoid artifacts from the starting model (e.g., Boehm et al., 2022; Métivier et al., 2016).…”

Section: Introductionmentioning

confidence: 99%

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Comparing Adjoint Waveform Tomography Models of California Using Different Starting Models

Afanasiev

Rodgers

Boehm³

et al. 2023

JGR Solid Earth

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Seismic tomography has been a vital tool for understanding Earth's interior structure since studies were first published in the late 1970s (e.g., Aki et al., 1977;Aki & Lee, 1976). Though the theory of Full waveform inversion (FWI) existed, ray-based travel time tomography methods were the primary method of velocity modeling for much of the field's history. Ray-based travel time tomography uses the difference between theoretical and observed arrival times of specified seismic waves to calculate velocity perturbations in the Earth (Dziewonski et al., 1977). Ray-based tomography can be computationally inexpensive but suffers in tectonically complex regions as the physics behind it is unable to resolve effects such as wavefront healing, focusing/defocusing, and other 3D wavefield effects (Liu & Gu, 2012;Rickers et al., 2012;Tarantola, 1984). Unlike ray-based methods, adjoint waveform tomography (AWT) accounts for 3D wavefield effects by solving the elastic wave equation through a given 3D volume, while also considering finite-frequency effects. AWT iteratively optimizes the synthetic data to best match the observed data for available source-receiver pairs. By using the recorded waveform instead of travel times, AWT includes more information (Romanowicz, 2003). AWT has a greater sensitivity to Earth structure than ray-based travel time tomography, enabling greater resolution of tectonic complexity.Uncertainty analysis and quantitative comparisons of FWI models continues to be a topic of active research (Flath et al.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Comparing Adjoint Waveform Tomography Models of California Using Different Starting Models

Afanasiev

Rodgers

Boehm³

et al. 2023

JGR Solid Earth

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“…Around the source, the FWI objective function shows rings, which can be explained by the so-called cycle-skipping. The reason for this is that the least squares objective function L only has a narrow parameter range where it is locally convex with respect to phase shifts in the signal [40]. Other error measures, such as cross-correlation, can mitigate this problem.…”

Section: Guided Wavesmentioning

confidence: 99%

Evaluation of inversion approaches for plates based on guided waves and modal analysis

Hoppe,

Schmid,

Kollofrath

et al. 2024

Discov Appl Sci

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The identification of defects in plate-like structures has been successfully treated using both local guided ultrasonic waves and global modal quantities. Although there are many papers on these techniques, a lack of comparability between the two methods persists. This makes it difficult for users to identify the most appropriate method for the defect in question. This paper examines the effect of different parameterizations of a circular defect in a square aluminum plate on the system response in a case study. The measured local ultrasound signal from a propagating guided wave makes up the initial data set. The first method uses the entire waveform for the objective function of the optimization problem, while the second considers the velocity of the $$A_0$$ A 0 mode. In the third and fourth methods, the first and second global natural frequencies of the plate modeled with free-free boundary conditions are investigated. The numerical models are validated experimentally through measurements with a laser Doppler vibrometer. This results in the qualitative and quantitative evaluation of the objective functions for all parameter combinations of the defect. The recommendation to sequentially employ modal analysis and then the ultrasound procedure is made for the defect type used in this study. The data gathered on the objective functions suggests that potential joint employment of the natural frequency and ultrasound methods may increase computational efficiency. For a specific case, the methods could also complement each other in terms of challenges such as local minima.

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“…Both L 2 and graph-space optimal transport 25,26 misfit functionals are used to compute the adjoint sources required to obtain the gradients ∇ c χ. The optimal transport misfit functional is able to effectively differentiate between discrepancies that stem from changes in both phase and amplitude between the two signals.…”

Section: Simulation Setupmentioning

confidence: 99%

Shape optimization for transcranial ultrasound computed tomography

Marty

Boehm

Fichtner

2023

Medical Imaging 2023: Ultrasonic Imaging and Tomography

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Using waveform-based inversion methods within transcranial ultrasound computed tomography is an attractive emerging reconstruction technique for imaging the human brain. However, such imaging approaches generally rely on possessing an accurate model of the skull in order to account for the complex interactions which occur when the ultrasound waves propagate between soft tissue and bone. In order to recover the shape of the skull within the context of full-waveform inversion, adjoint-based shape optimization is performed within this study. The gradients with respect to the acoustic properties of the tissues which are used in conventional full-waveform inversion act as a proxy for estimating the sensitivities to the shape of the skull. These shape derivatives can be utilized to update the interface between the interior brain tissue and the skull. This technique employs the spectral-element method for solving the wave equation and, thus, allows for the use of a convenient framework for representing the skull interfaces throughout the inversion. Adaptations of the Shepp-Logan phantom are used as a proof of concept to demonstrate this inversion strategy where both the shape of the skull as well as the interior brain tissue are imaged sequentially.

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Using optimal transport to mitigate cycle-skipping in ultrasound computed tomography

Cited by 9 publications

References 17 publications

Comparing Adjoint Waveform Tomography Models of California Using Different Starting Models

Comparing Adjoint Waveform Tomography Models of California Using Different Starting Models

Evaluation of inversion approaches for plates based on guided waves and modal analysis

Shape optimization for transcranial ultrasound computed tomography

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