Stabilizing the iterative solution to ultrasonic transmission tomography

Author

Song, Lin-ping ; Zhang, Shu-yi

Author_Institution

Inst. of Acoust., Nanjing Univ., China

Volume

45

Issue

4

fYear

1998

fDate

7/1/1998 12:00:00 AM

Firstpage

1117

Lastpage

1122

Abstract

A stable iterative reconstruction algorithm is presented for ultrasonic tomography through the uses of weighting matrices, damping factor, and the features of conjugate gradient method. The weighting matrices are chosen according to Berryman´s analysis of nonlinear tomography. An implicit conjugate gradient-type iterative formula is used to solve a weighted least-squares problem. In the iterative process, a damping factor of linear increase rather than a constant is used to filter out the influences of smaller singular values´ components. The results of simulated data show that our method can efficiently stabilize the iteration, and provide a robust solution.

Keywords

acoustic signal processing; acoustic tomography; conjugate gradient methods; image reconstruction; iterative methods; least squares approximations; numerical stability; singular value decomposition; ultrasonic imaging; Berryman analysis; conjugate gradient method; damping factor; iterative reconstruction algorithm; nonlinear tomography; singular value; stability; ultrasonic transmission tomography; weighted least squares; weighting matrix; Damping; Gradient methods; Iterative methods; Nonlinear filters; Reconstruction algorithms; Robustness; Tomography;

fLanguage

English

Journal_Title

Ultrasonics, Ferroelectrics, and Frequency Control, IEEE Transactions on

Publisher

ieee

ISSN

0885-3010

Type

jour

DOI

10.1109/58.710596

Filename

710596