Automating Regularization Parameter Selection of the Inverse Problem in Ultrasound Tomography

Ultrasound tomography (UT) is a noninvasive imaging modality that could be used to detect breast cancer. When compared to standard imaging techniques such as X-ray mammography, UT is cheaper, safer and better discerns dense breast tissue. One of the ways to reproduce the UT image is to use the Distorted Born Iterative (DBI) method. However, within each iteration of DBI an ill-posed inverse problems needs to be solved. This is a difficult task since standard regularization methods are not proven to be effective in most cases. Therefore, we use Tikhonov regularization in general form with our novel algorithm for choosing a regularization parameter λ. We test in simulations the robustness of our algorithm to changes in frequency. In addition, we provide the modification of the algorithm to achieve better reconstruction when lower levels of noise are considered in the measured data. The algorithm's efficiency is compared to a standard algorithm for obtaining regularization parameter: Generalized Cross Validation (GCV).