Ultrasonic Transmission Tomography Image Reconstruction Using Total Variation Regularization with Spilt Bregman Method

The total variation (TV) regularization method has good accuracy and edge preservation ability, and has been used to solve the inverse problem of ultrasonic transmission tomography (UTT). However, due to the need for multiple iterations of this method, the real-time performance of image reconstruction is often not ideal. To improve the speed of image reconstruction without sacrificing the accuracy of image reconstruction, a Split Bregman (SB) iterative solution for TV regularization method is proposed. This method is based on Bregman distance, which separates each variable in the constrained optimization equation independently and iteratively solves them separately. This method significantly reduces the number of iterations required for convergence and greatly accelerates the convergence speed of the TV method. The simulation and experimental results demonstrate that compared to using the Newton-Raphson algorithm to solve the inverse problem of the TV regularization method, the proposed SB algorithm reduces the computing time by an average of $73.68 \%$ and $72.26 \%$ in simulation and experiment, respectively.