Frequency-Domain Reconstruction of the Speed of Sound in Ring-Array Ultrasound Computed Tomography With Stochastic Phase Encoding.

The framework of ultrasound computed tomography (USCT) has recently reemerged 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 article, we present the equivalent stochastic inversion in the frequency domain [phase encoding (PE)], with a focus on reconstructing the speed of sound. We test our inversion algorithm on synthetic data and publicly available patient data, and compare against the deterministic inversion. By leveraging the concepts of multiple super-shots and stochastic ensembles, we provide robust evidence that the image quality of a stochastic reconstruction of the speed of sound with PE in the frequency domain is equivalent to that of a deterministic reconstruction, with the further benefit of drastically reducing reconstruction times. The algorithm described in this article is the most sophisticated USCT imaging algorithm and, at the time of writing, the fastest one solving the full waveform inversion (FWI) problem for the geometry of a ring array without any compromise to image quality. The imaging algorithm is portable to multiple tomographic geometries and paves the way to large-scale inversions in 3-D.