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

TY - JOUR

T1 - Frequency-Domain Reconstruction of the Speed of Sound in Ring-Array Ultrasound Computed Tomography with Stochastic Phase Encoding

AU - Forte, Luca A.

N1 - © 2026 IEEE.

PY - 2026/4/27

Y1 - 2026/4/27

N2 - 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 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 image quality of a stochastic reconstruction of the speed of sound with phase encoding in the frequency domain is equivalent to the one of a deterministic reconstruction, with the further benefit of drastically reducing reconstruction times. The algorithm described in this manuscript is the most sophisticated USCT imaging algorithm and, at the time of writing, the fastest one solving the full waveform inversion 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 3D.

AB - 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 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 image quality of a stochastic reconstruction of the speed of sound with phase encoding in the frequency domain is equivalent to the one of a deterministic reconstruction, with the further benefit of drastically reducing reconstruction times. The algorithm described in this manuscript is the most sophisticated USCT imaging algorithm and, at the time of writing, the fastest one solving the full waveform inversion 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 3D.

KW - ultrasound tomography

KW - full waveform inversion

KW - stochastic optimization

KW - breast imaging

U2 - 10.1109/TUSON.2026.3687801

DO - 10.1109/TUSON.2026.3687801

M3 - Article

SN - 3066-9464

JO - IEEE Transactions on Ultrasonics

JF - IEEE Transactions on Ultrasonics

ER -