Algorithm 1.

Initialize k̂(0). for i = 1, 2, … until convergence Set Q(i) equal to the rank-rC approximation of (k̂(i−1)). Set U(i) equal to the rank-rG approximation of (k̂(i−1)). Set V(i) equal to the rank-rS approximation of (k̂(i−1). Find k̂(i) by solving (34).

$$\begin{array}{c}{\widehat{\mathbf{k}}}^{(i)}=arg\underset{\mathbf{k}\in {ℂ}^S}{min}{\Vert \mathbf{Fk}-\mathbf{d}\Vert }_{{\ell }_2}^2+{\lambda }_{\mathbf{C}}{\Vert {\mathcal{P}}_{\mathbf{C}}(\mathbf{k})-{\mathbf{Q}}^{(i)}\Vert }_F^2\\ +{\lambda }_{\mathbf{G}}{\Vert {\mathcal{P}}_{\mathbf{G}}(\mathbf{k})-{\mathbf{U}}^{(i)}\Vert }_F^2+{\lambda }_{\mathbf{S}}{\Vert {\mathcal{P}}_{\mathbf{S}}(\mathbf{k})-{\mathbf{V}}^{(i)}\Vert }_F^2\end{array}$$ (34)