Table 2.

SoS estimation method

Set parameters

After reconstructing the IP image, the mean SoS along the ultrasound propagation path is known. The information provided by the mean SoS is not sufficient for back-projection based SoS estimation, so we use a model-based method to estimate the SoS distribution.

Set $n$ ($4<n<7$, empirically) points inside the phantom/animal trunk region. The SoS of these points is $\mathrm{\Lambda }=(v_1,v_2,\dots ,v_{\mathrm{n}})$, and generate the final SoS distribution map by natural interpolation.

An initial SoS $v_0$ could be chosen using other SoS compensation methods. Also, set the upper limit of the iteration number $N$, the iteration step $\tau$, and the SoS perturbation $\mathrm{\Delta }v$. Set the initial iteration number $k=1$.

Run SOS estimation

1. Given the SoS of several points ${\mathrm{\Lambda }}_{k-1}$, and calculate the SoS distribution map Ω(${\mathrm{\Lambda }}_{k-1}$) by natural interpolation.

2. Calculate the mean SoS along the ultrasound propagation path, mathematically $M(\mathrm{\Omega }(\mathrm{\Lambda }))=({\overline{v}}_1,{\overline{v}}_2,{\overline{v}}_3,\dots ,{\overline{v}}_{\mathrm{m}})$.

3. Calculate the correlation coefficient between $M(\mathrm{\Omega }(\mathrm{\Lambda }))$ and the mean SoS derived from the MSFC method; the correlation is written as $c({\mathrm{\Lambda }}_{k-1})$.

4. Add a perturbation $\mathrm{\Delta }v$ to ${\mathrm{\Lambda }}_{k-1}$, and calculate $c({\mathrm{\Lambda }}_{k-1}+\mathrm{\Delta }v)$ as described in 1, 2, and 3.

5. Calculate the gradient correlation coefficient $\nabla c({\mathrm{\Lambda }}_{k-1})=c({\mathrm{\Lambda }}_{k-1}+\mathrm{\Delta }v)-c({\mathrm{\Lambda }}_{k-1})$.

6. Compute the increment $\mu =\tau \nabla c({\mathrm{\Lambda }}_{\mathrm{k}-1})$.

7. ${\mathrm{\Lambda }}_k={\mathrm{\Lambda }}_{k-1}+\mu$

8. $k=k+1$.

9. if $k<N$, go to step 1; otherwise output the result Λ.