Algorithm 2. Alternating minimization for (6).

Input: ${\lambda }_1,{\lambda }_2,D$ , tolerance $ϵ$ , parameter $\delta$

Initialize: $S^{\left(1\right)}=0$

Repeat

Step 1. Obtain $L^{\left(k+1\right)}$ by Algorithm 1.

Step 2, Obtain $S^{\left(k+1\right)}$ by $P\left(\frac{1}{\sqrt{{\lambda }_2}}\left(D-L^{\left(k+1\right)}\right)\right)$

Until ${\Vert L^{\left(k+1\right)}-L^{\left(k\right)}\Vert }_F\le ϵ$

Output $L^{\left(k+1\right)}$ , $S^{\left(k+1\right)}$