Solving Ultrasound Tomography's Inverse Problem: Automating Regularization Parameter Selection

Ultrasound tomography (UT) is a noninvasive procedure that can be used to detect breast cancer. Yet, to accomplish this, reconstruction algorithms must solve an inherent nonlinear, ill-posed inverse problem. One solution is to use the distorted Born iterative (DBI) method. However, in order for succ...

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Bibliographic Details
Published in:IEEE transactions on ultrasonics, ferroelectrics, and frequency control Vol. 69; no. 8; pp. 2447 - 2461
Main Authors: Carevic, Anita, Slapnicar, Ivan, Almekkawy, Mohamed
Format: Journal Article
Language:English
Published: United States IEEE 01.08.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Distorted Born iterative (DBI) method
Ill posed problems
Image quality
Image reconstruction
Inverse problems
Iterative methods
Mathematical models
Noise levels
Numerical methods
Parameters
Regularization
Scattering
Tikhonov regularization
Tomography
Transducers
Ultrasonic imaging
ultrasound tomography (UT)
ISSN:0885-3010, 1525-8955, 1525-8955
Online Access:Get full text
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Summary:Ultrasound tomography (UT) is a noninvasive procedure that can be used to detect breast cancer. Yet, to accomplish this, reconstruction algorithms must solve an inherent nonlinear, ill-posed inverse problem. One solution is to use the distorted Born iterative (DBI) method. However, in order for successful convergence, ill-posed inverse problems must also be solved for each individual iteration. We used the Tikhonov regularization with different algorithms for choosing the regularization parameter that provides optimal balance, a solution neither overregularized nor underregularized. In this article, we propose a novel algorithm for choosing a balanced parameter based on minimizing two inversely proportional components: signal loss and scaled noise errors (SNEs). This begins with an overestimation of the noise in the measured data, which is then appropriately adjusted within each iteration of the DBI method using the discrepancy between measured and calculated data. We compared our algorithm to the L-curve method, as well as generalized cross-validation (GCV) and projection-based regularized total least-squares (PB-RTLS) methods. Four numerical simulations with varying noise levels and aperture settings showed that our algorithm provided the lowest relative error (RE) for phantom reconstruction, signifying image quality compared to the other methods.
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ISSN:0885-3010
1525-8955
1525-8955
DOI:10.1109/TUFFC.2022.3182147