Time-domain spectral-element ultrasound waveform tomography using a stochastic quasi-Newton method

Christian Boehm*, Naiara Korta Martiartu, Nicolas Vinard, Ivana Jovanovic Balic, Andreas Fichtner

*Corresponding author for this work

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

18 Citations (Scopus)


Waveform inversion for ultrasound computed tomography (USCT) is a promising imaging technique for breast cancer screening. However, the improved spatial resolution and the ability to constrain multiple parameters simultaneously demand substantial computational resources for the recurring simulations of the wave equation. Hence, it is crucial to use fast and accurate methods for numerical wave propagation, on the one hand, and to keep the number of required simulations as small as possible, on the other hand. We present an efficient strategy for acoustic waveform inversion that combines (i) a spectral-element continuous Galerkin method for solving the wave equation, (ii) conforming hexahedral mesh generation to discretize the scanning device, (iii) a randomized descent method based on mini-batches to reduce the computational cost for misfit and gradient computations, and (iv) a trust-region method using a quasi-Newton approximation of the Hessian to iteratively solve the inverse problem. This approach combines ideas and state-of-the-art methods from global-scale seismology, large-scale nonlinear optimization, and machine learning. Numerical examples for a synthetic phantom demonstrate the efficiency of the discretization, the effectiveness of the mini-batch approximation and the robustness of the trust-region method to reconstruct the acoustic properties of breast tissue with partial information.

Original languageEnglish
Title of host publicationMedical Imaging 2018
Subtitle of host publicationUltrasonic Imaging and Tomography
ISBN (Electronic)9781510616493
Publication statusPublished - 1 Jan 2018
EventMedical Imaging 2018: Ultrasonic Imaging and Tomography - Houston, United States
Duration: 10 Feb 201815 Feb 2018


ConferenceMedical Imaging 2018: Ultrasonic Imaging and Tomography
Country/TerritoryUnited States


  • spectral-element method
  • stochastic L-BFGS
  • ultrasound tomography
  • waveform inversion


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