Regularization in ultrasound tomography using projection-based regularized total least squares

Mohamed Khaled Almekkawy, Anita Carević, Ahmed Abdou, Jiayu He, Geunseop Lee, Jesse Louis Barlow

Research output: Contribution to journalArticle

Abstract

Ultrasound Tomography (UT) is primarily used for the detection of malignant tissue in the human breast. However, the reconstruction algorithms used for UT require large computational time and are based upon solving a nonlinear, ill-posed inverse problem. We constructed and solved the inverse scattering problem from UT using the Distorted Born Iterative method. Since this problem is ill-posed, this paper focuses on optimizing the reconstruction method by analysing and selecting a better regularization algorithm to solve the inverse problem. The performance of two regularization algorithms, Truncated Total Least Squares (TTLS) and a Projection-Based Regularized Total Least Squares (PB-RTLS), are compared. The advantages of using PB-RTLS over TTLS are the dimension reduction of the problem being solved and the avoidance of the SVD calculation. These results in significant decrease of computational time. The dimension reduction is achieved by projecting the problem onto lower dimensional subspace, where the subspace is expanded dynamically by employing a generalized Krylov subspace expansion. In addition, PB-RTLS is avoiding the problem associated with finding the truncation parameter in TTLS since it has integrated parameter search. We proved using simulated and breast phantoms that PB-RTLS has lower relative error which results in better reconstructed images.

Original languageEnglish (US)
JournalInverse Problems in Science and Engineering
DOIs
StatePublished - Jan 1 2019

Fingerprint

Total Least Squares
Ultrasound
Tomography
Regularization
Ultrasonics
Projection
Inverse problems
Singular value decomposition
Iterative methods
Dimension Reduction
Scattering
Inverse Problem
Tissue
Subspace
Krylov Subspace
Inverse Scattering Problem
Reconstruction Algorithm
Ill-posed Problem
Phantom
Relative Error

All Science Journal Classification (ASJC) codes

  • Engineering(all)
  • Computer Science Applications
  • Applied Mathematics

Cite this

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title = "Regularization in ultrasound tomography using projection-based regularized total least squares",
abstract = "Ultrasound Tomography (UT) is primarily used for the detection of malignant tissue in the human breast. However, the reconstruction algorithms used for UT require large computational time and are based upon solving a nonlinear, ill-posed inverse problem. We constructed and solved the inverse scattering problem from UT using the Distorted Born Iterative method. Since this problem is ill-posed, this paper focuses on optimizing the reconstruction method by analysing and selecting a better regularization algorithm to solve the inverse problem. The performance of two regularization algorithms, Truncated Total Least Squares (TTLS) and a Projection-Based Regularized Total Least Squares (PB-RTLS), are compared. The advantages of using PB-RTLS over TTLS are the dimension reduction of the problem being solved and the avoidance of the SVD calculation. These results in significant decrease of computational time. The dimension reduction is achieved by projecting the problem onto lower dimensional subspace, where the subspace is expanded dynamically by employing a generalized Krylov subspace expansion. In addition, PB-RTLS is avoiding the problem associated with finding the truncation parameter in TTLS since it has integrated parameter search. We proved using simulated and breast phantoms that PB-RTLS has lower relative error which results in better reconstructed images.",
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Regularization in ultrasound tomography using projection-based regularized total least squares. / Almekkawy, Mohamed Khaled; Carević, Anita; Abdou, Ahmed; He, Jiayu; Lee, Geunseop; Barlow, Jesse Louis.

In: Inverse Problems in Science and Engineering, 01.01.2019.

Research output: Contribution to journalArticle

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