## 4 Results
The figure and table indicate that the CNR and SNR improvements in lateral strain achieved through STREAL enhancement are highly remarkable. More particularly, Figure 6 shows that, through STREAL enhancement, the lateral strain image obtained with the AM2D estimator transforms from almost an entirely noisy image to a relatively high-quality image where the inclusion is highly distinguishable. This is confirmed by the data given in Table 5, which shows that the CNR and SNR were increased by factors of over 20 and 1.6 times, respectively. It is noteworthy that the [PERSON]'s modulus ratios are not reported in the table, as lateral strains do not provide a good estimate of this ratio due to the high spatial variability of the stresses in the lateral direction. For evaluating the performance of the displacement estimators with and without STREAL enhancement on clinical data, constructed [PERSON]'s modulus, axial strain, and lateral strain images pertaining to 3 patients in the dataset are presented. Figures 7-9 show images of the reconstructed [PERSON]'s modulus, axial strain, and lateral strain, respectively, for Patient 1. Similarly, Figures 10-12 show images of the reconstructed [PERSON]'s modulus, axial strain, and lateral strain, respectively, for Patient 2, while Figures 13-15 show images of the reconstructed [PERSON]'s modulus, axial strain, and lateral strain, respectively, for Patient 3. Each reconstruction is associated with a table of CNR, SNR, and ratio (Tables 6-8). Generally, the quality of all images generated using the OVERWIND estimator is poor compared to images generated using other estimators. Except for the OVERWIND estimator, other estimators led to reasonably high-quality images. Among AM2D, GLUE, and SOUL estimators, AM2D led to noisier images, while preserving necessary information, including stiffness values and tumor shape. This once again indicates the advantage of the AM2D estimator, which has much higher computational efficiency at the cost of losing little image quality. Like the phantom case, it is also observed that STREAL enhancement has the highest influence on lateral strain images with all estimators. Again, this enhancement transforms almost entirely noisy lateral strain images into high-quality images where both tumor shape and its stiffness can be estimated. For lateral strain images, the STREAL enhancement in conjunction with AM2D, GLUE, and SOUL estimators demonstrates remarkable improvement, as this enhancement transforms very low-quality images into images where the tumors are quite distinguishable. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Displacement Estimator** & **CNR** & **CNR** & **SNR** & **SNR** & **Ratio** & **Ratio** \\
**Estimator** & **Pre-STREAL** & **Post-STREAL** & **Pre-STREAL** & **Post-STREAL** & **Pre-STREAL** & **Post-STREAL** \\ \hline AM2D & 32.9 & 658.0 & 14.7 & 416.7 & 1.8 & 2.7 \\ \hline GLUE & 15.2 & 15.7 & 5.5 & 5.9 & 1.6 & 1.6 \\ \hline OVERWIND & 42.0 & 42.2 & 15.3 & 15.0 & 1.6 & 1.6 \\ \hline SOUL & 9.8 & 10.6 & 2.1 & 2.2 & 1.3 & 1.3 \\ \hline \end{tabular}
\end{table} 
Table 6: CNR, SNR, and Inclusion to background Young’s modulus ratios obtained for axial strain images of Patient 1 computed using each displacement estimator with and without STREAL enhancement. Figure 8: Axial strain images of Patient 1 computed from displacement fields obtained by each displacement estimator with and without STREAL enhancement. AM2D provides reasonably high-quality images at a very low computational cost. Figure 9: Lateral strain images of Patient 1 computed from displacement fields obtained by each displacement estimator with and without STREAL enhancement. AM2D with STREAL enhancement provides reasonably high-quality images at a very low computational cost. Figure 11: Axial strain images of Patient 2 computed from displacement fields obtained by each displacement estimator with and without STREAL enhancement. AM2D provides reasonably high-quality images at a very low computational cost.