## 2 Materials and Methods
### Multi-look Based Compressive Sensing Layover Separation Method  
In the compressive sensing method based on multi-look, the pixels around the current point are treated as independent observations together with this point. Additionally, multi-look operations assume that all scatterers in the neighborhood (looks) around the current point exhibit the same height. The advantage of this method is that it increases the tolerance of the L2 norm minimization part in Equation (7), so as to improve the stability of the target point elevation inversion by reducing the noise level [21]. Assuming that the number of looks in multi-look processing is \(P\), the discrete model of this method can be expressed as:  
\[G=M\gamma+\varepsilon \tag{8}\]  
where \(\gamma\) and \(\varepsilon\) are the \(K\times P\) matrix, and the observed vector \(G\) with the \(K\times P\) matrix has  
\[G= \begin{bmatrix}g_{11}&g_{12}&\cdots&g_{1P}&\cdots&g_{K1}&g_{K2}&\cdots&g_{KP} \end{bmatrix} ^{T} \tag{9}\]  
where \(g_{ij}\) represents the observed value of the look j in the antenna i (i = 1:\(K\), j = 1:\(P\)). The measurement matrix \(M\) is the matrix of \(W\times N\) (\(W=K\times P\)), and it can be expressed as  
\[M= \begin{bmatrix}A_{11,1}&A_{11,2}&\cdots&A_{11,N}\\ A_{12,1}&A_{12,2}&\cdots&A_{12,N}\\ \vdots&\vdots&\ddots&\vdots\\ A_{1P,1}&A_{1P,1}&\cdots&A_{1P,1}\\ \vdots&\vdots&\ddots&\vdots\\ A_{1P,1}&A_{1P,1}&\cdots&A_{1P,1}\\ \vdots&\vdots&\ddots&\vdots\\ A_{1P,1}&A_{1P,1}&\cdots&A_{1P,1}\end{bmatrix}  \tag{10}\]  
where \(A_{ij,l}\) represents the measurement value of the current height value l of the look number j of the antenna i (i = 1:\(K\), j = 1:\(P\)), and it can be expressed as  
\[A_{ij,l}=\exp\biggl{(}j\frac{2\pi}{\lambda}\cdot\frac{B_{i}\cos(\theta_{l}- \alpha)}{R\sin(\theta_{l})}\cdot h_{l}\biggr{)} \tag{11}\]  
In this case, Equation (6) becomes  
\[\hat{\gamma}=\operatorname*{argmin}_{\gamma}\left\|\gamma\right\|_{1}\quad s.t. \quad\left\|G-M\gamma\right\|_{2}<\varepsilon \tag{12}\]  
According to the calculation method of L1 norm, the value \(\varepsilon\) can be projected onto the noise subspace of corresponding singular values by means of Singular Value Decomposition (SVD). \[M=U\Sigma V^{T} \tag{13}\]  
where \(U= \begin{bmatrix}u_{1}&u_{2}&\cdots&u_{K\times P}\end{bmatrix} \) and \(V= \begin{bmatrix}v_{1}&v_{2}&\cdots&v_{N}\end{bmatrix} \) are the unitary matrix vectors of SVD, and the main diagonal of \(\Sigma\) comprises non-negative singular values in descending order. If the dimensions of the signal subspace are determined to be equivalent to the number of w scattering points in layover areas [20], the noise \(\varepsilon\) can be expressed as  
\[\varepsilon=\sqrt{\frac{P\times K}{P\times K-w}\sum_{n=w+1}^{P\times K}|u_{n}^ {T}G|} \tag{14}\]  
Since the multi-look processing method increases the dimensions of the measurement matrix, the number of singular values of M is \(K\times P\), while the number of singular values of \(A\) in Equation (5) is only \(K\). Obviously, when the dimensions of signal subspace are unchanged in the same pixel of layover areas, the dimensions of the \(M\) noise subspace are increased, and the noise level obtained by projection onto the observation vector \(G\) will be more robust. Therefore, multi-look processing improves the stability of the sparsity solution in compressive sensing. Meanwhile, it can be seen in Equation (3) whose L1 norm is equivalent to the L0 norm of compressive sensing, that after multi-look processing, the dimensions of K are improved, and the establishment of Equation (3) will be more robust. Thus, the processing method of L1 norm is closer to the solution of L0 norm, and the sparsity solving ability is enhanced. In other words, the layover separation method based on multi-look compressive sensing provides the L1 norm solution method with more sparsity, a stronger ability to separate scatterers and a higher accuracy of the obtained results by increasing the observation vector.