### 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 language | English (US) |
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Journal | Inverse Problems in Science and Engineering |

DOIs | |

State | Published - Jan 1 2019 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

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

### Cite this

*Inverse Problems in Science and Engineering*. https://doi.org/10.1080/17415977.2019.1628227

}

**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.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Regularization in ultrasound tomography using projection-based regularized total least squares

AU - Almekkawy, Mohamed Khaled

AU - Carević, Anita

AU - Abdou, Ahmed

AU - He, Jiayu

AU - Lee, Geunseop

AU - Barlow, Jesse Louis

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85067546645&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85067546645&partnerID=8YFLogxK

U2 - 10.1080/17415977.2019.1628227

DO - 10.1080/17415977.2019.1628227

M3 - Article

AN - SCOPUS:85067546645

JO - Inverse Problems in Science and Engineering

JF - Inverse Problems in Science and Engineering

SN - 1741-5977

ER -