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

Abstract

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.