Algorithm 1 IALM-RPCA [60].
Input: XCA data matrix D, λ.
1:	Initialize: L, S, X.
2:	while not converged do
3:	L sub-problem:
	$L_{k+1}={\text{argmin}}_L\mathcal{L}\left(L,S_k,X_k\right)$
	$={\text{argmin}}_L\Vert L{\Vert }_{*}+\frac{\mu }{2}{\Vert D_k-L-S_k+X_k/\mu \Vert }_F^2$
	solved by:
	(U, Σ, V) = SVD(Dk – Sk + Xk/μ);
	$L_{k+1}=U{S}_{{(\mu )}^{-1}}(\Sigma )V^T;$
4:	S sub-problem:
	$S_{k+1}={\text{argmin}}_S\mathcal{L}\left(L_{k+1},S,X_k\right)$
	$={\text{argmin}}_S\lambda {\Vert S\Vert }_1+\frac{\mu }{2}{\Vert \left(D-L_{k+1}+X_k/\mu \right)-S\Vert }_F^2,$
	solved by:
	Sk+1 = Sλ/μ(D − Lk+1 + Xk/μ);
5:	Xk+1 = Xk+μ(D − Lk+1 + Sk+1);
6:	k = k + 1;
7:	end while
Output: Initial background layer L, initial vessel layer S.