# Improved Acoustic Emission Tomography Algorithm Based on Lasso Regression
## 6 Discussion  
In this experiment, because the defect of the specimen was exceptionally narrow and long instead of sparse and scattered distribution, the elastic emission wave bypassed the defected part and then reached the receivers during the transmission process according to the basic theory of the ray-trace technique in AE tomography. The velocity on the left side of the defected area was displayed as a significant high-velocity distribution, because the  
Figure 17: Reconstructed velocity distribution: (**a**) result by the SIRT algorithm adopting 36 events; (**b**) result by the LASSO algorithm adopting 18 events. Figure 18: Flowchart of AE tomography in different imaging methods. \begin{table}
\begin{tabular}{c c} \hline \hline
**Traditional SIRT Algorithm** & **Proposed LASSO Algorithm** \\ \hline Request a sufficient number of events & Request few events \\ High rates of measurement paths & Lower rates of measurement paths \\ Velocity distribution with shadows & Few shadows in the velocity distribution \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of the characteristics of different algorithms. real ray paths through this area were crossed with a length close to that through the non-defected area, rather than theoretically through the defective area, as shown in Figure 19. On the contrary, the elastic emissions wave needed to bypass the entire defective part to reach the receivers with long-distance propagations on the right half of the model, resulting in a low-velocity range in the right half since the wave propagation time increased. In AE tomography technology, the exact elastic wave emission position is unknown, it needs to estimate time and the source location and then identify the velocity distribution. As a consequence, AE tomography is a technique that can detect the realistic condition of velocity distribution for defect area identification in the real world. It is noted that the residual error between the observed and calculated travel times should be zero in intact microstructure theoretically, because the distance between the event point to receivers and the velocity on a homogeneity medium were identical. However, there was a discrepancy between the observed and theoretical travel times of the elastic wave propagating through the unbroken region in the experiment due to the existence of refraction and diffraction. The algorithms of the SIRT calculated each divided element iteratively, with the intact mesh cells affected during the iteration which is why the flawless part had shadows in elastic velocity distribution. In the LASSO algorithm, these entire areas were occupied by the majority of the model where the travel time residual is also described as infinitely close to zero. This means that the intact part was affected very little during the calculation; hence, the original velocity distribution in the intact part was almost maintained. In the calculation involving the defect area, which was described as low-velocity cells, due to the influence of \(\lambda\) in Equation (10), where \(\lambda\) is the regularization parameter and equal to the calculated extreme value under the constraints in the function. The damaged area described as low-velocity regions in the velocity reconstruction was sharpened and pronounced. Compared with the SIRT algorithm, the LASSO algorithm could identify a more distinguishable elastic velocity distribution, since the optimal local solution was solved subject to a minimum sum of residual errors that are not zero. Last but not least, according to the simulation of the L1 algorithm capability in actual simulation and experimental results, the characteristics and applicability of the proposed theory in practice can be summarized as follows: (1) the damage location of the structure could be tracked when the defect range was already known to be less than about 30% of the total model in the condition.