Employing methods with generalized singular value decomposition for regularization in ultrasound tomography

Anita CareviA, Ahmed Abdou, Ivan Slapniaar, Mohamed Almekkawy

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

4 Scopus citations


The Distorted Born Iterative (DBI) method is used for ultrasound tomography in order to localize and identify malignant breast tissues. This approach begins with the Born approximation to generate an initial prediction of the scattering function. Then, iteratively solves the forward problem for the total field and the inhomogeneous Green's function, and the inverse problem for the scattering function. The drawback of this method is that the associated inverse scattering problem is ill-posed. We are proposing the Truncated General Singular Value Decomposition (TGSVD) approach as a regularization method for the ill posed inverse problem Xy = b in DBI and comparing it to the well known Truncated Singular Value Decomposition (TSVD). The TGSVD employs generalized SVD (GSVD) of matrix pair (X,L) and is neglecting the smallest, contaminated with noise, generalized singular values, while regularization matrix L (we used the first order derivative operator) is responsible for smoothing the solution. This results in better image quality. We compared the performances of these two methods on simulated phantom and proved that TGSVD produces lower relative error and better reconstructed image.

Original languageEnglish (US)
Title of host publicationMedical Imaging 2019
Subtitle of host publicationUltrasonic Imaging and Tomography
EditorsNicole V. Ruiter, Brett C. Byram
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

All Science Journal Classification (ASJC) codes

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


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