## 4 Results  
For each displacement estimator, with and without refinement using the STREAL method, Figure 2 illustrates errors in the reconstructed inclusion-to-background [PERSON]'s modulus ratios, Hausdorff distances between the truth and reconstructed outlines of the inclusion, and MSE between ground truth and reconstructed [PERSON]'s modulus images obtained for the phantoms' datasets. Statistical significance (\(p<0.05\)) between results generated by pairs of displacement estimators, both with and without refinement using the STREAL method, is also indicated in this figure. As seen in this figure, the AM2D displacement estimator with STREAL enhancement provides the most accurate inclusion-to-background [PERSON]'s modulus reconstruction ratio, while, on average, the STREAL enhancement reduces this error to less than one third compared to its pre-enhancement counterpart. The AM2D estimator with enhancement also leads to improved MSE, while  
Figure 1: A flow chart demonstrating the iterative reconstruction process described in [33; 42]. The [PERSON]’s moduli(E) is iteratively re-calculated using measured strains until convergence is achieved, where convergence is defined as the mean absolute difference obtained from two consecutive iterations and is less than a specified tolerance (0.01). its Hausdorff distance is not significantly different from other estimators. The latter implies that, compared to other estimators, while AM2D improves the quantitative distribution of the [PERSON]'s modulus ratio significantly, it does not improve the estimated shape of the inclusion significantly. When applied to synthetic data, the AM2D estimator provides accurate inclusion to background [PERSON]'s modulus ratio error estimation while preserving the quality of inclusion shape (Hausdorff distance). It generally compares well with the ground truth [PERSON]'s modulus distribution according to the small MSE values and very high specificity, sensitivity, and Kappa statistics, as can be seen in Table 2. In terms of runtime, however, AM2D ranges around 0.1 s, whereas GLUE, OVERWIND, and SOUL are approximately 8 s, 20 s, and 40 s, respectively. To demonstrate/compare the quality of the reconstructed [PERSON]'s modulus, Figure 3 illustrates an example obtained through processing a synthetic data sample. As can be seen, the AM2D estimator provides a high-quality reconstruction of the [PERSON]'s modulus when combined with STREAL enhancement. The \"ground truth\" reconstruction image was obtained by processing the ground truth displacement field, which was used to find the displacements of scatterers, using the iterative [PERSON]'s modulus reconstruction algorithm described earlier. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Displacement Estimator** & **Specificity Pre-STREAL** & **Specific Post-STREAL** & **Sensitivity Pre-STREAL** & **Sensitivity Post-STREAL** & **Kappa Statistic Pre-STREAL** & **Kappa Statistic Post-STREAL** \\ \hline AM2D & 0.99 \(\pm\) 0.004 & 0.99 \(\pm\) 0.006 & 0.96 \(\pm\) 0.02 & 0.97 \(\pm\) 0.03 & 0.92 \(\pm\) 0.02 & 0.91 \(\pm\) 0.02 \\ \hline GLUE & 0.99 \(\pm\) 0.005 & 0.98 \(\pm\) 0.007 & 0.95 \(\pm\) 0.04 & 0.95 \(\pm\) 0.05 & 0.90 \(\pm\) 0.02 & 0.88 \(\pm\) 0.03 \\ \hline OVERWIND & 0.99 \(\pm\) 0.005 & 0.98 \(\pm\) 0.006 & 0.93 \(\pm\) 0.03 & 0.93 \(\pm\) 0.05 & 0.90 \(\pm\) 0.03 & 0.88 \(\pm\) 0.03 \\ \hline SOUL & 0.99 \(\pm\) 0.007 & 0.98 \(\pm\) 0.008 & 0.94 \(\pm\) 0.02 & 0.94 \(\pm\) 0.04 & 0.86 \(\pm\) 0.03 & 0.85 \(\pm\) 0.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Specificity, sensitivity, and kappa statistics for the agreement of thresholded inclusions of each displacement estimator compared to the ground truth. Figure 2: Errors in reconstructed inclusion-to-background Young’s modulus ratios, Hausdorff distances between truth and reconstructed outlines of the inclusion, and MSE between ground truth and reconstructed Young’s modulus images obtained using the four displacement estimation methods of AM2D, GLUE, OVERWIND, and SOUL with and without STREAL enhancement.