# Adaptive Bat Algorithm Optimization Strategy for Observation Matrix
## 5 Conclusions  
As we know, it is critical to select an appropriate observation matrix to ensure high signal reconstruction accuracy. In this paper, an adaptive bat algorithm is proposed to optimize the observation matrix. To improve the global search ability, the position of the optimal solution is updated continuously by designing the adaptive bat algorithm search method. Further, the adaptive bat algorithm is used to optimize the observation matrix. Finally, we verify our model on four different signals, the optimized observation matrix and the smaller reconstruction error value are obtained. The simulation results fully show that the adaptive bat algorithm optimization observation matrix can obtain higher signal reconstruction accuracy and better robustness, compared with other algorithms. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Signal**} & \multirow{2}{*}{**Rate**} & \multirow{2}{*}{**Data**} & \multicolumn{2}{c}{**DHT**} & \multicolumn{2}{c}{**FFT**} \\ \cline{3-6}  & & & **Gaussian** & **ABA** & **Gaussian** & **ABA** \\ \hline \multirow{6}{*}{\(S_{1}\)} & \multirow{2}{*}{0.30} & _RE_ & \(4.5714\times 10^{-14}\) & \(\mathbf{3.6916\times 10^{-14}}\) & \(4.0586\times 10^{-15}\) & \(\mathbf{3.1462\times 10^{-15}}\) \\ \cline{3-6}  & & _PI_ & \(19.25\%\) & **–** & \(22.48\%\) & **–** \\ \cline{2-6}  & \multirow{2}{*}{0.35} & _RE_ & \(4.3217\times 10^{-14}\) & \(\mathbf{3.4521\times 10^{-14}}\) & \(3.8985\times 10^{-15}\) & \(\mathbf{3.1030\times 10^{-15}}\) \\ \cline{3-6}  & & _PI_ & \(20.12\%\) & **–** & \(20.41\%\) & **–** \\ \cline{2-6}  & \multirow{2}{*}{0.40} & _RE_ & \(4.2001\times 10^{-14}\) & \(\mathbf{3.4700\times 10^{-14}}\) & \(3.8786\times 10^{-15}\) & \(\mathbf{3.1139\times 10^{-15}}\) \\ \cline{3-6}  & & _PI_ & \(17.38\%\) & **–** & \(19.72\%\) & **–** \\ \cline{2-6}  & \multirow{2}{*}{0.45} & _RE_ & \(4.1711\times 10^{-14}\) & \(\mathbf{3.3844\times 10^{-14}}\) & \(3.8565\times 10^{-15}\) & \(\mathbf{3.0513\times 10^{-15}}\) \\ \cline{3-6}  & & _PI_ & \(18.86\%\) & **–** & \(20.88\%\) & **–** \\ \cline{2-6}  & \multirow{2}{*}{0.50} & _RE_ & \(4.1014\times 10^{-14}\) & \(\mathbf{3.3120\times 10^{-14}}\) & \(3.8174\times 10^{-15}\) & \(\mathbf{3.0155\times 10^{-15}}\) \\ \cline{3-6}  & & _PI_ & \(19.25\%\) & **–** & \(21.01\%\) & **–** \\ \hline \multirow{6}{*}{\(S_{3}\)} & \multirow{2}{*}{0.30} & _RE_ & \(6.5552\times 10^{-14}\) & \(\mathbf{5.0519\times 10^{-14}}\) & \(6.1340\times 10^{-15}\) & \(\mathbf{4.6387\times 10^{-15}}\) \\ \cline{3-6}  & & _PI_ & \(22.93\%\) & **–** & \(24.38\%\) & **–** \\ \cline{2-6}  & \multirow{2}{*}{0.35} & _RE_ & \(6.5499\times 10^{-14}\) & \(\mathbf{4.9979\times 10^{-14}}\) & \(5.9468\times 10^{-15}\) & \(\mathbf{4.4886\times 10^{-15}}\) \\ \cline{3-6}  & & _PI_ & \(23.70\%\) & **–** & \(24.50\%\) & **–** \\ \cline{2-6}  & \multirow{2}{*}{0.40} & _RE_ & \(6.4900\times 10^{-14}\) & \(\mathbf{4.8152\times 10^{-14}}\) & \(5.7716\times 10^{-15}\) & \(\mathbf{4.3008\times 10^{-15}}\) \\ \cline{3-6}  & & _PI_ & \(25.81\%\) & **–** & \(25.48\%\) & **–** \\ \cline{2-6}  & \multirow{2}{*}{0.45} & _RE_ & \(6.4718\times 10^{-14}\) & \(\mathbf{4.7886\times 10^{-14}}\) & \(5.6797\times 10^{-15}\) & \(\mathbf{4.2642\times 10^{-15}}\) \\ \cline{3-6}  & & _PI_ & \(26.01\%\) & **–** & \(24.92\%\) & **–** \\ \hline \multirow{6}{*}{\(0.50\)} & _RE_ & \(6.4152\times 10^{-14}\) & \(\mathbf{4.7102\times 10^{-14}}\) & \(5.4878\times 10^{-15}\) & \(\mathbf{4.1672\times 10^{-15}}\) \\ \cline{3-6}  & & _PI_ & \(26.58\%\) & **–** & \(24.06\%\) & **–** \\ \hline \hline \end{tabular}  
* The bold indicates that signals can be reconstructed with better results under different observation matrices and transform bases.  
\end{table} 
Table 4: Reconstruction effect of different observation matrices and transform bases. **Funding:** This work is supported by the National Natural Science Foundation of China under Grant No.61806138, No.