Algorithm 1 Iteratively re-weighted minimization of Total-Variation (IRTV-Lq)

$$\begin{array}{cc}\hfill 1:& {\mathbf{u}}^{(0)}=({\mathbf{H}}^T\mathbf{H}+{\lambda }^{(0)}{\mathbf{I}}^T\mathbf{I}{)}^{-1}{\mathbf{H}}^T\varphi ▷\mathbf{Initialization}\mathbf{u}\hfill \\ \hfill 2:& k=1▷\mathbf{Initialization}k\hfill \\ \hfill 3:& \mathbf{while}\Vert TV({\mathbf{u}}^{(k)})-TV({\mathbf{u}}^{(k-1)}){\Vert }_2\le tol,\hfill \\ \hfill 4:& tol={10}^{-3}\hfill \\ \hfill 5:& \mathbf{do}\hfill \\ \hfill 6:& {\widehat{\mathbf{u}}}^{(k)}=({\mathbf{H}}^T\mathbf{LH}+{\lambda }^{(k)}{\tilde{\mathbf{W}}}^T\tilde{\mathbf{W}}{)}^{-1}{\mathbf{H}}^T\mathbf{L}\varphi \hfill \\ \hfill 7:& {\tilde{\mathbf{W}}}^T\tilde{\mathbf{W}}=\sum \begin{array}{c}N\hfill \\ i=1\hfill \end{array}\frac{\nabla {\phi }_i^T\nabla {\phi }_i}{\mid \nabla {\phi }_i{\mathbf{u}}^{(k-1)}\mid +\beta }\hfill \\ \hfill 8:& {\lambda }^{(k)}=\frac{\Vert {\mathbf{H}}^T\mathbf{LH}{\Vert }_{\infty }}{\Vert {\sum }_{i=1}^N\frac{\nabla {\phi }_i^T\nabla {\phi }_i}{\mid \nabla {\phi }_i{\mathbf{u}}^{(k-1)}\mid +\beta }{\Vert }_{\infty }},\hfill \\ \hfill 9:& \mathbf{if}q=2\mathbf{then},▷\mathbf{IRTV}\text{-}L2\hfill \\ \hfill 10:& \mathbf{L}=\mathbf{I}(\text{Identity matrix});\hfill \\ \hfill 11:& \mathbf{end}\mathbf{if}\hfill \\ \hfill 12:& \mathbf{if}q=1\mathbf{then},▷\mathbf{IRTV}\text{-}L1\hfill \\ \hfill 13:& \mathbf{L}={\mathbf{W}}_f^T{\mathbf{W}}_f=diag({\mathbf{Hu}}^{(k-1)}-\varphi )\hfill \\ \hfill 14:& \mathbf{end}\mathbf{if}\hfill \\ \hfill 15:& k=k+1\hfill \\ \hfill 16:& \mathrm{end}\mathrm{while}\hfill \end{array}$$