# The Feasibility of Shadowed Image Restoration Using the Synthetic Aperture Focusing Technique
## 4 Discussion  
At present, there is no relevant research which explores the potential lesions lying in acoustic shadow; a differential diagnosis is the best that can be done [7; 17]. This current research is the first use of SAFT to reveal the existence of an object that is in the acoustic shadow. In addition, to simulate human tissue, this study uses water as the medium and monofilament to perform immersed scans. The low acoustic impedance contrast between water and the monofilament line thus degrades the laboratory data. However, satisfying results are still being achieved, providing effective information for the future development of ultrasonic detection methods. Before directly applying SAFT to the laboratory data, a synthetic pitch/catch scan profile is computed, based on point reflection/diffraction theory. Eight targets of different spatial positions are purposely arranged. In Figure 3a, the theoretical echo signals that can be detected from the created targets show up as eight hyperbolic trajectories. To simulate a shadowed image, part of the echo signals from three of the targets, i.e., T\({}_{1}\), T\({}_{2}\), and T\({}_{3}\), are purposely silenced. Once the synthetic image is SAFT-processed, Figure 3b demonstrates the output. In Figure 3b, it can be seen that the original images of all created targets, T\({}_{\text{OBS}}\) and T\({}_{\text{N}}\), are perfectly reconstructed and repositioned. Restoration is also expected for the shadowed targets. The technique requires a partial or distorted signal for the restoration algorithm to reliably reconstruct the shadowed object. In particular, a sufficient amount \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**B-Mode Scan**} \\ \hline \multicolumn{2}{c}{\(\mathbf{SP_{\text{OBS}}}\)} & \multicolumn{3}{c}{\(\mathbf{SP_{\text{FR}}}\)} \\ \hline \(\mathbf{T_{\text{OBS}}}\) & 41.3/37.5 (\(\upmu\)s) & 40.8/40.7 (\(\upmu\)s) & T\({}_{4}\) \\
30.0/27.25 (mm) & 27.5/27.2 (mm) & 29.6/29.5 (mm) & 30.0/29.65 (mm) \\ \hline T\({}_{1}\) & & 48.7/48.7 (\(\upmu\)s) & T\({}_{5}\) \\
38.0/37.65 (mm) & & 36.8/36.8 (mm) & 38.0/37.65 (mm) \\ \hline T\({}_{2}\) & & 61.1/61.1 (\(\upmu\)s) & T\({}_{6}\) \\
46/45.65 (mm) & & 44.3/44.3 (mm) & 46/45.65 (mm) \\ \hline T\({}_{3}\) & 77.6/80.0 (\(\upmu\)s) & 78.1/80.2 (\(\upmu\)s) & T\({}_{7}\) \\
58/57.65 (mm) & 56.3/58.0 (mm) & 56.7/58.1 (mm) & 58/57.65 (mm) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Details of the original observations (raw data) and SAFT-processed data for the B-mode scan (Figure 3). Numbers shown below the targets (T\({}_{\text{OBS}}\) and T\({}_{\text{N}}\)) are the depths of the centers and the tops of the relative holes (center/top). Numbers above the slash of relative imaged echoes show the information of original observations and those below the slash are obtained from the results of the SAFT process. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**Pitch/Catch Scan**} \\ \hline \multicolumn{2}{c}{\(\mathbf{SP_{\text{OBS}}}\)} & \multicolumn{3}{c}{\(\mathbf{SP_{\text{FR}}}\)} \\ \hline \(\mathbf{T_{\text{OBS}}}\) & 40.1/37.7 (\(\upmu\)s) & 43.5/41.7 (\(\upmu\)s) & T\({}_{4}\) \\
30.0/27.25 (mm) & 29.1/27.3 (mm) & 31.6/30.2 (mm) & 30.0/27.25 (mm) \\ \hline T\({}_{1}\) & & 53.5/51.6 (\(\upmu\)s) & T\({}_{5}\) \\
38.0/37.65 (mm) & & 38.8/37.4 (mm) & 38.0/37.65 (mm) \\ \hline T\({}_{2}\) & 63.3/60.8 (\(\upmu\)s) & 63.6/61.9 (\(\upmu\)s) & T\({}_{6}\) \\
46/45.65 (mm) & 46.1/44.1 (mm) & 46.1/44.9 (mm) & 46/45.65 (mm) \\ \hline T\({}_{3}\) & 79.8/77.5 (\(\upmu\)s) & 81.1/81.0 (\(\upmu\)s) & T\({}_{7}\) \\
58/57.65 (mm) & 57.8/56.2 (mm) & 5.8/58.8 (mm) & 58/57.65 (mm) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Details of the original observations (raw data) and SAFT-processed data for the pitch/catch mode scan (Figure 4). Numbers shown below the targets (T\({}_{\text{OBS}}\) and T\({}_{\text{N}}\)) are the depths of the centers and the tops of the relative holes (center/top).