# Spaceborne Sparse SAR Imaging Mode Design: From Theory to Implementation
## 4 Experiments and Discussion  
To validate the performance of the designed modes, some experiments are performed based on the parameters of the designed sparse Sliding Spotlight and Scan modes (see Tables 1 and 2). The experiments are implemented in MATLAB version R2023b and on a computer with a 3.0 GHz Intel i9 processor and an NVIDIA GeForce RTX 4090 GPU. In the experiment of the Sliding Spotlight imaging mode, the computation times of MF, the \(L_{q}\)-norm regularization-based method, and the \(L_{2,q}\)-norm regularization-based method are 11.62 s, 74.67 s, and 230.92 s, respectively. For the Scan mode experiment, the running times of above three methods are 1.62 s, 10.13 s, and 27.68 s, respectively, which are consistent with the theoretical analysis of computational complexity in [40]. In the experiments, selecting an appropriate iteration step size enabled satisfactory results to be achieved within five iterations. Figures 11 and 12 show the recovered images of different kinds of surveillance areas by MF, \(L_{q}\)-norm regularization-based and \(L_{2,q}\)-norm regularization-based methods from the collected echo data of the designed sparse modes (\(q=1\)). For comparison, Figures 11a and 12a depict the MF-based images recovered from the data collected by the traditional Sliding Spotlight and Scan modes (parameters are in Tables 1 and 2). In Scan mode, the parameters of the SS1 subswath are used as an example for verification. Since the PRF satisfies the requirements of the sampling theorem, it is found that MF can effectively achieve high-quality recovery of the considered sparse scenes. But for the designed sparse modes, it fails to recover the sparse scenes with obvious ambiguities and energy dispersion along the azimuth direction (see Figures 11b and 12b). Compared with MF-based results, as shown in Figures 11c and 12c, the recovered images of the \(L_{q}\)-norm regularization-based method are well focused with better performance. However, they still suffer from the azimuth ambiguities, which lead to false alarms and inaccurate interpretation. In comparison, the \(L_{2,q}\)-norm regularization-based sparse imaging method consistently achieves unambiguous recovery of the surveillance region, even when the data are collected with a reduced PRF in sparse modes (see Figures 11d and 12d). To further verify the proposed method, the target-to-ambiguity ratio (TAR) and target-to-background ratio (TBR) are introduced to quantitatively evaluate the ambiguity and noise suppression ability of different methods, which are defined as  
\[\text{TAR} \triangleq 10\log_{10}\left(\frac{\sum_{(np,nq)\in\mathcal{M}}\left|\mathbf{ X}(np,nq)\right|^{2}}{\sum_{(np,nq)\in\mathcal{A}_{i}}\left|\mathbf{X}(np,nq) \right|^{2}}\right) \tag{21}\]  
\[\text{TBR} \triangleq 10\log_{10}\left(\frac{\sum_{(np,nq)\in\mathcal{T}}\left|\mathbf{ X}(np,nq)\right|^{2}}{\sum_{(np,nq)\in\mathcal{B}}\left|\mathbf{X}(np,nq) \right|^{2}}\right) \tag{22}\]  
where \(\mathcal{M}\) denotes the main imaging area, \(\mathcal{A}_{i}\) is the \(i\)th azimuth ambiguity area with \(i\in\mathbb{Z}^{-}\) and \(i\in\mathbb{Z}^{+}\) being the shifting indexes of ambiguity areas in the left and right sides of the main imaging area in the azimuth direction, respectively, and \(\mathcal{B}\) indicates the background region around the target area \(\mathcal{T}\). The TAR and TBR values of the recovered images in Figures 11 and 12 are shown in Table 3, respectively. From Table 3, it is seen that compared with MF and the \(L_{q}\)-norm regularization-based methods, the \(L_{2,q}\)-norm regularization-based sparse SAR imaging method suppresses the azimuth ambiguity dramatically in the designed sparse modes and hence obtains images with higher SCNR. Figure 11: Reconstructed images of ships by different methods from the data collected by the sparse Sliding Spotlight mode. (**a**) MF (traditional parameters). (**b**) MF. (**c**) \(L_{q}\)-norm regularization-based sparse imaging method. (**d**) \(L_{2,q}\)-norm regularization-based sparse imaging method.