## 4 Phase Denoise Experiment and Result
### Result of Synchronization Phase Denoising  
During the training of the dictionary, the corresponding parameters are listed in Table 2. A regular overlap is maintained between the phase segments to eliminate the jitter  
Figure 6: (**a**) Synchronization phase of LT-1A \(\varphi_{\text{ba}}\) and LT-1B \(\varphi_{\text{ab}}\). (**b**) Internal calibration compensation phase \(\varphi_{\text{cal}}\). Figure 7: STD of residual phase error versus SNR of synchronization signal. caused by phase splicing. Smaller sparsity threshold and error tolerance can train a better over-complete dictionary, but at the cost of training time. The higher-order term of imaging phase difference is input. The initial RS transform matrix and the trained sparse dictionary are shown in Figure 8. Each phase segment can be represented by a series of atoms in the adaptive learning dictionary. By splicing all phase segments, the original phase can be reconstructed with high precision. Once the dictionary is trained, it can be applied to other synchronization data one the ground or in orbit. Taking a group of data with the lowest SNR (38 dB) as an example, the synchronization compensation phase after denoising is shown in Figure 9. Kalman filtering is also implemented for comparison [37]. The phase details in Figure 9b show that the denoising results are closer to the imaging phase difference, which indicate that both methods can effectively reduce the noise level of synchronization compensation phase. However, through careful observation, it can be found that the distance from Kalman filtered phase to the imaging phase difference is a little farther than that from the denoised phase by CS to the imaging phase difference. In addition, the Kalman filtered result shifts slightly to the right relative to the imaging phase difference. The reason for this hysteresis phenomenon is that the Kalman filter estimates the state by combining the observed and predicted values, where the predicted values are based on the previous state estimate. Thus, a time delay is inevitable. While the sparse reconstruction is based on the prior information in the dictionary, which is why it can reduce noise as much as possible without introducing time delay. The residual phases after synchronization compensation in Figure 10 intuitively show the denoising performance. It is obvious that the residual phase of CS method is smaller than that of KF method. The phase statistical histogram of corresponding residual error is shown in the right side. The probability density function (PDF) indicates that the residual phase error conforms to the Gaussian distribution. The STD of residual error before denoising is 0.6163\({}^{\circ}\). After Kalman filtering, STD drops to 0.3015\({}^{\circ}\). The phase denoising method based on CS further reduces the STD to 0.2273\({}^{\circ}\), which verifies its effectiveness. To verify the effect of phase synchronization and phase denoising on SAR images, azimuth impulse response compression experiments are carried out. The parameters of the LT-1 system and the residual phases in Figure 10 are used for simulation experiments, and \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Value** \\ \hline Phase segment length & \(n\) & 64 \\ Phase segment overlap rate & \(r\) & 50\% \\ Number of the atoms & \(k\) & 256 \\ Sparsity threshold & \(m\) & 4 \\ Error tolerance & \(\varepsilon\) & 0.1\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of K-SVD Dictionary Training. Figure 8: Matrix of the dictionary. (**a**) RS transform matrix. (**b**) Trained sparse dictionary. the experimental results are shown in Table 3. When the phase error exists, the peak position is shifted due to the influence of the linear phase. The side lobes become asymmetric due to the influence of the higher-order phase. The peak phase error is quite large, which is unacceptable for bistatic interferometry. In addition, the phase error also reduces the peak amplitude.