Algorithm 1 RPCA algorithm

Input:  $\mathbf{M}$ 1:procedure  Compute RPCA 2:    ${\mathbf{S}}_0={\mathbf{Y}}_0=\mathbf{0}$ 3:    repeat 4:        Compute ${\mathbf{L}}_k={\mathcal{D}}_{1/\mu }(\mathbf{M}-{\mathbf{S}}_{k-1}+{\mu }^{-1}{\mathbf{Y}}_{k-1})$ 5:        Compute ${\mathbf{S}}_k={\mathcal{S}}_{\lambda /\mu }(\mathbf{M}-{\mathbf{L}}_k+{\mu }^{-1}{\mathbf{Y}}_{k-1})$ 6:        Compute ${\mathbf{Y}}_k={\mathbf{Y}}_{k-1}+\mu (\mathbf{M}-{\mathbf{L}}_k-{\mathbf{S}}_k)$ 7:    until $\parallel \mathbf{M}-{\mathbf{L}}_k-{\mathbf{S}}_k\parallel$ < tolerance 8:end procedure Output:  ${\mathbf{L}}_k$, ${\mathbf{S}}_k$                           ▹k = last computed step