## 4 Development of Proposed Method
### Proposed Method
#### 4.2.5 Signal Reconstruction
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **SNR** & \multicolumn{2}{c}{**VMD-DFA**} & **VMD-DFA-DWT** & **Proposed Method** \\ \hline \multirow{6}{*}{Piecewise-regular} & \multirow{2}{*}{0} & Mean & \(-6.876\) & \(-6.645\) & \(-\mathbf{12.38}\) \\  & & SD & \(0.6480\) & \(0.3404\) & \(0.7005\) \\  & & Median & \(-6.754\) & \(-6.523\) & \(-12.36\) \\ \cline{2-6}  & \multirow{2}{*}{10} & Mean & \(-16.74\) & \(-16.99\) & \(-\mathbf{20.55}\) \\  & & SD & \(0.4537\) & \(0.5532\) & \(0.3992\) \\  & & Median & \(-16.76\) & \(-16.87\) & \(-20.42\) \\ \cline{2-6}  & \multirow{2}{*}{20} & Mean & \(-24.71\) & \(-25.77\) & \(-\mathbf{26.68}\) \\  & & SD & \(0.3031\) & \(0.5964\) & \(0.6117\) \\  & & Median & \(-24.69\) & \(-25.91\) & \(-26.91\) \\ \hline \multirow{6}{*}{Doppler} & \multirow{2}{*}{0} & Mean & \(-6.229\) & \(-6.373\) & \(-\mathbf{11.51}\) \\  & & SD & \(0.3175\) & \(0.2938\) & \(0.4041\) \\  & & Median & \(-6.140\) & \(-6.344\) & \(-11.41\) \\ \cline{2-6}  & \multirow{2}{*}{10} & Mean & \(-16.25\) & \(-11.87\) & \(-\mathbf{18.94}\) \\  & & SD & \(0.3615\) & \(0.6128\) & \(0.2605\) \\  & & Median & \(-16.25\) & \(-11.75\) & \(-18.93\) \\ \cline{2-6}  & \multirow{2}{*}{20} & Mean & \(-20.50\) & \(-12.47\) & \(-\mathbf{25.59}\) \\  & & SD & \(0.7927\) & \(0.0831\) & \(0.3333\) \\  & & Median & \(-20.24\) & \(-12.48\) & \(-25.63\) \\ \hline \multirow{6}{*}{HeavySine} & \multirow{2}{*}{0} & Mean & \(-6.358\) & \(-6.881\) & \(-\mathbf{13.63}\) \\  & & SD & \(0.2079\) & \(0.6277\) & \(0.5074\) \\  & & Median & \(-6.374\) & \(-6.733\) & \(-13.68\) \\ \cline{2-6}  & \multirow{2}{*}{10} & Mean & \(-16.40\) & \(-16.37\) & \(-\mathbf{22.34}\) \\  & & SD & \(0.2184\) & \(10.19\) & \(0.5706\) \\  & & Median & \(-16.48\) & \(-16.34\) & \(-22.30\) \\ \cline{2-6}  & \multirow{2}{*}{20} & Mean & \(-26.38\) & \(-26.29\) & \(-\mathbf{29.97}\) \\  & & SD & \(0.2712\) & \(0.4136\) & \(0.3729\) \\  & & Median & \(-26.46\) & \(-26.36\) & \(-30.01\) \\ \hline \multirow{6}{*}{Blocks} & \multirow{2}{*}{0} & Mean & \(-6.228\) & \(-6.430\) & \(-\mathbf{12.32}\) \\  & & SD & \(0.1611\) & \(0.3146\) & \(0.5460\) \\  & & Median & \(-6.215\) & \(-6.473\) & \(-12.43\) \\ \cline{2-6}  & \multirow{2}{*}{10} & Mean & \(-15.59\) & \(-16.43\) & \(-\mathbf{19.91}\) \\  & & SD & \(0.1708\) & \(0.2275\) & \(0.4708\) \\  & & Median & \(-15.60\) & \(-16.54\) & \(-19.88\) \\ \cline{2-6}  & \multirow{2}{*}{20} & Mean & \(-21.99\) & \(-\mathbf{23.83}\) & \(-23.22\) \\  & & SD & \(0.4978\) & \(0.5250\) & \(0.5207\) \\  & & Median & \(-22.16\) & \(-24.13\) & \(-23.34\) \\ \hline \multirow{6}{*}{Bumps} & \multirow{2}{*}{0} & Mean & \(-6.719\) & \(-6.609\) & \(-\mathbf{12.14}\) \\  & & SD & \(0.2399\) & \(0.3565\) & \(0.5303\) \\  & & Median & \(-6.682\) & \(-6.643\) & \(-12.01\) \\ \cline{2-6}  & \multirow{2}{*}{10} & Mean & \(-16.88\) & \(-16.48\) & \(-\mathbf{20.52}\) \\  & & SD & \(0.4923\) & \(0.6016\) & \(0.4111\) \\  & & Median & \(-19.71\) & \(-16.66\) & \(-20.42\) \\ \cline{2-6}  & \multirow{2}{*}{20} & Mean & \(-25.71\) & \(-26.35\) & \(-\mathbf{28.75}\) \\  & & SD & \(0.4054\) & \(0.6414\) & \(0.2901\) \\  & & Median & \(-25.79\) & \(-26.19\) & \(-29.61\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Quantitative results for test signals: NMSE (expressed in dB) for various VMD-based denoising methods for different input SNR levels.