Open-source Gauss-Newton-based methods for refraction-corrected ultrasound computed tomography

Rehman Ali, Scott Hsieh, Jeremy Dahl

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


This work presents refraction-corrected sound speed reconstruction techniques for transmission-based ultrasound computed tomography using a circular transducer array. Pulse travel times between element pairs can be calculated from slowness (the reciprocal of sound speed) using the eikonal equation. Slowness reconstruction is posed as a nonlinear least squares problem where the objective is to minimize the error between measured and forward-modeled pulse travel times. The Gauss-Newton method is used to convert this problem into a sequence of linear least-squares problems, each of which can be efficiently solved using conjugate gradients. However, the sparsity of ray-pixel intersection leads to ill-conditioned linear systems and hinders stable convergence of the reconstruction. This work considers three approaches for resolving the ill-conditioning in this sequence of linear inverse problems: 1) Laplacian regularization, 2) Bayesian formulation, and 3) resolution-filling gradients. The goal of this work is to provide an open-source example and implementation of the algorithms used to perform sound speed reconstruction, which is currently being maintained on Github: rehmanali1994/

Original languageEnglish (US)
Title of host publicationMedical Imaging 2019
Subtitle of host publicationUltrasonic Imaging and Tomography
EditorsBrett C. Byram, Nicole V. Ruiter
ISBN (Electronic)9781510625570
StatePublished - 2019
EventMedical Imaging 2019: Ultrasonic Imaging and Tomography - San Diego, United States
Duration: Feb 17 2019Feb 18 2019

Publication series

NameProgress in Biomedical Optics and Imaging - Proceedings of SPIE
ISSN (Print)1605-7422


ConferenceMedical Imaging 2019: Ultrasonic Imaging and Tomography
Country/TerritoryUnited States
CitySan Diego


  • Bayesian
  • Gauss-Newton method
  • Nonlinear inverse problems
  • Regularization
  • Resolution-lling

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Biomaterials
  • Atomic and Molecular Physics, and Optics
  • Radiology Nuclear Medicine and imaging


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