## 6 Numerical Results
### Measurement-Formation and Reconstruction of OTD Datasets with the Proposed Termination Rule  
In order to verify the effectiveness of the proposed adaptive termination rule, we select the two OTD datasets (depicted in Figure 1) as the original experimental signal. Due to the influence of \(\Delta M\) on the performance of this algorithm, we carry out the experiment on the number of measurements and the quality of signal reconstruction under different \(\Delta M\) conditions. With the purpose of ensuring the accuracy of the experimental results, we repeat the experiment of each set of parameters 500 times, and the detailed experimental parameters are listed in Table 3.  
Figure 12 shows an execution process (\(\Delta M=8  
By comparing the experimental results of these two time-continuous datasets, we find that the number of required measurements is different (_i.e._, the number for OTD-B is less than that of OTD-A), which is due to their different sparsity degrees (as shown in Figure 1, the sparsity degree of OTD-B is higher than that of OTD-A, _i.e._, 53-sparse and 61-sparse, respectively). With the increase of \(\Delta M\), the average number of measurements required by the two datasets will increase rapidly (_i.e._, OTD-A increases by 106.5% and OTD-B increases by 59%). The minimum and maximum number indexes also show a similar phenomenon. The reason is that with the increase of \(\Delta M\) (_i.e._, the increase of measurement required by each round of reconstruction (\(\Delta M\)) also grows), according to the conclusion of Proposition 1, it is more difficult to meet the measurement termination condition under that situation. Another typical characteristic is that at the beginning of increasing \(\Delta M\), the SNR of reconstructed signal increases rapidly; but when the SNR reaches a certain level, further increasing \(\Delta M\) has little effect. For example, for dataset OTD-A, when \(\Delta M=1\), Min SNR = 22.9, and when \(\Delta M=4\), SNR is up to 40.49; if continuing to increase \(\Delta M\) to 8, the corresponding SNR becomes 43.5. This feature is caused by \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{2}{*}{\(\Delta M\)} & \multirow{2}{*}{**DataSet**} & \multicolumn{3}{c}{**Number of Measurements**} & \multicolumn{3}{c}{**Relative Error of Results**} & \multirow{2}{*}{**MIN SNR**} \\ \cline{3-3} \cline{5-10}  & & **AVG** & **MIN** & **MAX** & **AVG** & **MIN** & **MAX** & \\ \hline \multirow{2}{*}{1} & A & 143.43 & 103 & 198 & 0.1042 & 0.0139 & 0.4568 & 22.9357 \\  & B & 141.60 & 103 & 180 & 0.1202 & 0.0110 & 0.4504 & 22.2775 \\ \hline \multirow{2}{*}{2} & A & 189.26 & 118 & 274 & 0.0225 & 0.0068 & 0.1527 & 34.1279 \\  & B & 181.07 & 156 & 210 & 0.0152 & 0.0056 & 0.0517 & 37.0925 \\ \hline \multirow{2}{*}{3} & A & 222.04 & 160 & 283 & 0.0131 & 0.0069 & 0.0445 & 38.2235 \\  & B & 196.70 & 169 & 226 & 0.0102 & 0.0045 & 0.0197 & 40.3772 \\ \hline \multirow{2}{*}{4} & A & 246 & 180 & 316 & 0.0098 & 0.0057 & 0.0175 & 40.4925 \\  & B & 211.73 & 176 & 244 & 0.0066 & 2.1694 \(\times 10^{-8}\) & 0.0115 & 47.3546 \\ \hline \multirow{2}{*}{5} & A & 256.85 & 175 & 330 & 0.0090 & 0.0051 & 0.0212 & 41.2457 \\  & B & 213.33 & 165 & 265 & 0.0065 & 4.6999 \(\times 10^{-10}\) & 0.0144 & 48.6981 \\ \hline \multirow{2}{*}{6} & A & 276.22 & 202 & 334 & 0.0078 & 0.0043 & 0.0135 & 42.3482 \\  & B & 225.20 & 196 & 262 & 0.0047 & 4.5934 \(\times 10^{-11}\) & 0.0078 & 62.4401 \\ \hline \multirow{2}{*}{7} & A & 286.69 & 219 & 338 & 0.0070 & 0.0043 & 0.0127 & 43.3284 \\  & B & 220.87 & 184 & 254 & 0.0052 & 6.7932 \(\times 10^{-11}\) & 0.0118 & 64.2592 \\ \hline \multirow{2}{*}{8} & A & 296.24 & 212 & 356 & 0.0069 & 0.0040 & 0.0132 & 43.4967 \\  & B & 225.07 & 188 & 268 & 0.0049 & 1.3999 \(\times 10^{-10}\) & 0.0105 & 69.4010 \\ \hline \end{tabular}
\end{table} 
Table 4: Experiment result of our proposed method performed on OTD datasets. Figure 13: Experiment process (\(\Delta M=8\)) of our proposed method on OTD datasets.