Pulse-echo sound speed estimation based on a Nakagami model of the echo amplitude

This work explores the use of the Nakagami model of the backscattered echo signal amplitude as an indirect assessment of image sharpness to estimate soft tissue sound speed c_t. This method exploits the relationship between the Nakagami model shape parameter m and the number of scatterers within the resolution cell. The parameter m is used to track changes in the size of the ultrasound system´s point spread function as the beamformer sound speed in a commercial ultrasound system, c_bf, is varied. The estimation performance of m is compared to a direct measure of image sharpness, i.e., the size S_c of the echo intensity correlation cell. The proposed method is tested on two tissue mimicking phantoms corresponding to fatty and non-fatty soft tissues. The phantoms were scanned with low- and high-frequency linear array transducers. Keeping the transducers fixed on the scanning window of each phantom, 19 radiofrequency data frames of the same phantom plane were acquired with c_bf varying symmetrically about the expected c_t, The amount of echo data to estimate S_c was first optimized. Then both m and S_c were estimated from echo data with different c_bf. The c_bf values at which m and S_c were minimized were chosen as c_t estimates. Statistics of c_t estimates were obtained by scanning independent phantom planes. Results show that both m and S_c are minimized when c_bf is close to c_t. Bias of c_t estimates from the high-frequency transducer was smaller than the bias from the low frequency transducer. The Nakagami parameter m gradually increased up to a value of m=1 as S_c increased. This results from reaching the Rayleigh scattering limit. The Nakagami parameter is attractive due to its estimation simplicity.