Stochastic Reconstruction of the Speed of Sound in Breast Ultrasound Computed Tomography with Phase Encoding in the Frequency Domain

The framework of ultrasound computed tomography (USCT) has recently re-emerged as a powerful, safe and operator-independent way to image the breast. State of the art image reconstruction methods are performed with iterative techniques based on deterministic optimization algorithms in the frequency domain in the 300 kHz - 1 MHz bandwidth. Alternative algorithms with deterministic and stochastic optimization have been considered in the time-domain. In this paper, we present the equivalent stochastic inversion in the frequency domain (phase encoding), with a focus on reconstructing the speed of sound. We test the inversion algorithm on synthetic data in 2D and 3D, by explicitly differentiating between inverse crime and non-inverse crime scenarios, and compare against the deterministic inversion. We then show the results of the stochastic inversion in the frequency domain on experimental data. By leveraging on the concepts of multiple super-shots and stochastic ensembles, we provide robust evidence that image quality of a stochastic reconstruction of the speed of sound with phase encoding in the frequency domain is comparable, and essentially equivalent, to the one of a deterministic reconstruction, with the further benefit of drastically reducing reconstruction times by more than half.