Fourier energy spectrum centroid: a robust and efficient approach for shear wave speed estimation in ω - k space.

Objective. The propagation speed of a shear wave, whether externally or internally induced, in biological tissues is directly linked to the tissue's stiffness. The group shear wave speed (SWS) can be estimated using a class of time-of-flight (TOF) methods in the time-domain or phase speed-based methods in the frequency domain. However, these methods suffer from biased estimations or time-consuming computations, and they are especially prone to wave distortions in in vivo cases. In this work, we present a parameter-free, robust, and efficient group SWS estimation method coined as Fourier energy spectrum centroid (FESC). Approach. The proposed FESC method is based on the center of mass inω-kspace. It was evaluated on data from computer simulations with additive Gaussian noise, a commercial elasticity phantom, an ex vivo pig liver, and in vivo biceps brachii muscles of three young healthy male subjects. The FESC method was compared with two 2D frequency-domain methods: Max-fre, which considers phase SWS at the peak of k -space, and Fre-regre, which applies linear regression of phase SWS within a fixed bandwidth. Two additional benchmarks included time-domain methods based on cross-correlation (X-Corr) and radon sum transformation (RD). Main results. Statistical results showed that our FESC method and the RD method had comparable accuracy and robustness, outperforming the other benchmark methods. In the simulation and phantom studies, when the signal-to-noise ratio was higher than 25 dB, our FESC showed higher accuracy than RD. In the in vivo study, our FESC method had better repeatability than RD. Furthermore, the proposed FESC method was 100 times faster than the runner-up method, X-Corr, and 3,000 times faster than the least efficient method, RD. Significance. All results indicated that our proposed Fourier-based method shows promise in reliably and efficiently providing reference values for group SWS in homogeneous bulk media.
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