## 2 Materials and Methods
### Traditional Compressive Sensing Method Based on L1 Norm for Layover Separation  
Nowadays, the classical compressive sensing method based on L1 norm is the Basic Pursuit (BP) algorithm based on L1 norm proposed by [PERSON] et al. [16], which has been widely verified by experiments in spaceborne SAR (TerraSAR-X) tomography. This paper briefly introduces the algorithm, which transforms the L0 norm into L1 norm to solve the optimization.  
Assuming that \(K\) is the dimension of the observation vector, \(L\) is the number of non-zeros in the sparse signal, and \(Q\) is the length of the original signal, the L1 norm optimization can obtain the same result as the L0 norm optimization when the following Equation (3) is met.  
\[K=O(L\cdot\log(Q/L)) \tag{3}\]  
Figure 1: Layover model of multi-baseline SAR.  
In this case, the L1 norm solution can be expressed as:  
\[\hat{\gamma}=\underset{\gamma}{\text{argmin}}\|\gamma\|_{1}\quad s.t.\quad g= \Theta\gamma \tag{4}\]  
Since the sensing matrix \(A\) is a Fourier matrix, choosing the basis matrix of the unitary matrix \(\Psi\) can obtain the best incoherent performance. Therefore, the measurement matrix becomes \(\Theta=A\cdot I=A\), and Equation (4) becomes:  
\[\hat{\gamma}=\underset{\gamma}{\text{argmin}}\|\gamma\|_{1}\quad s.t.\quad g=A\gamma \tag{5}\]  
Under the condition of measurement noise, Equation (5) becomes:  
\[\hat{\gamma}=\underset{\gamma}{\text{argmin}}\|\gamma\|_{1}\quad s.t.\quad\|g- A\gamma\|_{2}<\varepsilon \tag{6}\]  
where \(\varepsilon\) represents the noise level.  
Equation (6) can be equivalent to:  
\[\hat{\gamma}=\underset{\gamma}{\text{argmin}}\Big{\{}\|g-A\gamma\|_{2}^{2}+ \lambda_{k}\|\gamma\|_{1}\Big{\}} \tag{7}\]  
where \(\lambda_{k}\) is the regularization constant related to noise.  
Equations (6) and (7) can be used to solve the layover problems by means of the Basic Pursuit algorithm and this method does not need to acquire measurement data to obtain a better scattering point separation ability. Moreover, the results of the Basic Pursuit algorithm have certain values at the corresponding height of the scatterer, while it is zero at the height of the non-scatterer, and there is no interference from the sidelobe. Therefore, more stable results can be obtained, and the resolution ability of the scatterer height at the layover is also stronger compared with spectral estimation method and the maximum likelihood estimation method. Although this method produces a more stable solution with a large number of baselines or passes (at least greater than 6), in the case of airborne multiple baselines, due to the small number of baselines (2-3), the Restricted Isometry Property (RIP) and the incoherence of this method are poor, and it is difficult to produce stable and credible results [20]. In [20], the distributed scatterer compressive sensing and multi-look compressive sensing methods are, respectively, simulated and compared with the traditional L1 norm compressive sensing methods, and it is concluded that the distributed compressive sensing and multi-look compressive sensing methods can achieve more stable results under the airborne multi-baseline SAR system, but no experiments with measured data are carried out.  
Therefore, this paper refers to the multi-look concept and adds it to the traditional L1 compressive sensing method to bring its estimation results closer to the solution of the L0 norm, which can improve RIP characteristics and incoherence, and make the height direction measurement of scattering points in layover areas more stable and reliable. Later simulation and measured data processing are used to verify the improved effect of the multi-look concept on the traditional L1-norm compressed sensing method.