## 3 Results
### Numerical Simulations
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Method** & **[Axial, Lateral]** & **[Axial, Lateral]** & **FWHM (mm)** & **Signal-to-Clutter Ratio (dB)** \\ \hline \multirow{3}{*}{Simulation (flat bone)} & Conventional & [1.34, 0.42] & 1.27 \(\pm\) 0.20 & 54.7 \(\pm\) 1.1 \\ \cline{2-5}  & Phase-screen & [1.31, 0.37] & 1.09 \(\pm\) 0.21 & 58.7 \(\pm\) 2.1 \\ \cline{2-5}  & Geometry-based & [0.03, 0.14] & 1.01 \(\pm\) 0.14 & 63.6 \(\pm\) 1.9 \\ \hline \multirow{3}{*}{Simulation (realistic bone)} & Conventional & [1.26, 0.90] & 1.55 \(\pm\) 0.52 & 44.9 \(\pm\) 2.2 \\ \cline{2-5}  & Phase-screen & [1.05, 0.85] & 1.41 \(\pm\) 0.28 & 49.2 \(\pm\) 3.0 \\ \cline{2-5}  & Geometry-based & [0.08, 0.64] & 1.16 \(\pm\) 0.47 & 51.6 \(\pm\) 3.1 \\ \hline \multirow{3}{*}{Sawbones plate} & Conventional & [2.23, 0.80] & 2.26 \(\pm\) 0.80 & 45.1 \(\pm\) 5.3 \\ \cline{2-5}  & Phase-screen & [2.12, 0.76] & 1.30 \(\pm\) 0.17 & 44.1 \(\pm\) 6.0 \\ \cline{2-5}  & Geometry-based & [0.15, 0.10] & 1.20 \(\pm\) 0.28 & 51.6 \(\pm\) 5.62 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Quantitative evaluation of the numerical and experimental results presented in Figures 4, 6 and 7. Figure 6: _Cont._  
Figure 5c shows the reconstructed image by the PS method when the AP used for phase aberration correction by the PS method is estimated with a heterogeneous background wave-speed model. Many scatterers (see the yellow boxes) are undetectable due to the low accuracy of the aberration profile estimation. As shown in Figure 6f, the focused RF data of the second scatterer (acting as the beacon signal for patch two; see Figure 3c) are better distinguished from the background speckle noise (caused by variation in the background wave-speed speed) compared to the focused RF data of the first scatterer (see Figure 6b). This helps with better estimating the aberration profile and results in better reconstruction of the scatterers in patch 2 compared to patch 1 (Figure 5c). Speckle noise affects each A-line  
Figure 6: Estimation of the aberration profile with the numerical dataset generated with the flat bone model and a heterogeneous background. The wavefront backscattered from (**a**) scatterer #1 and (**e**) scatterer #2; a tilted plane wave (by 7.5 degrees in cutaneous tissue) was used for excitation. The numerical wavefront backscattered by (**b**) scatterer #1 and (**f**) scatterer #2 after synthetic transmit focusing on the locations of scatterer #1 and #2, respectively, by coherent compounding of the RF data generated by 5 tilted plane waves (from \(-\)15 to 15 degree in cutaneous tissue). (**c,g**) The extracted wavefront using triangulation for scatterer (**c**) #1 and (**g**) #2. The estimated phase shift (aberration profile) in nanoseconds for scatterer (**d**) #1 and (**h**) #2. Figure 7: The reconstructed numerical images using (**a**) conventional beamforming, (**b,c**) phase-screen modeling, and (**d**) geometry-based reconstruction techniques with a realistic bone model (Figure 3b, based on the micro CT of a real human temporal bone). The aberration profile was estimated using a dataset generated with a (**b**) homogeneous and (**c**) heterogeneous background wave-speed model. The red dots indicate the true location of the scatterers. The lateral FWHM (**e**), the signal-to-clutter ratio (**f**), and the localization error (**g**) obtained with all the methods for each scatterer. and the reference beamsum signal (which is generated by summation over the A-lines recorded by all the elements of the array), and, consequently, the AP estimation; compare the AP in Figures 2d and 6g and the fine AP in Figures 2g and 6h. The irregular near and far surfaces of the realistic human temporal bone model (see Figure 3b) degrade the image reconstructed by all the methods. Meanwhile, nearly all the scatterers are detected in the image reconstructed by the GB method (see Figure 7d); most scatterers are not detected by the PS method when the AP is estimated with a homogeneous background (see Figure 7b).