Naslov
Regularization in Ultrasound Tomography using Projection Based Regularized Total Least Squares

Autori
Almekkawy, Mohamed ; Carević, Anita ; Abdou, Ahmed ; He, Jiayu ; Lee, Geunseop ; Jesse Barlow

Izvornik
Inverse problems in science and engineering (1741-5977) 27 (2019); 1-24

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Inverse problem, Regularization, Ultrasound tomography, Distotred Born iterative method

Sažetak
Ultrasound Tomography (UT), a useful tool for medical diagnosis, 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 in- verse scattering problem from UT using the Distorted Born Iterative (DBI) method. Since this problem is ill-posed, this paper focuses on optimizing the reconstruction method by analyzing 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. In addition, results show that it takes significantly less computational time than TTLS.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Računarstvo

POVEZANOST RADA