Algorithm 1 The proposed algorithm by combining group sparsity and nonlocal self-similarity.

Input:    measured terahertz data y, observation matrix R, sparsity basis ${\mathrm{\Psi }}_p^{2D}$, nonlocal self-similarity operator ${\mathrm{\Psi }}_p^{3D}$.

Initialization:    ${\mathit{\alpha }}_p^0={\mathbf{\Theta }}_p^0={\mathit{b}}_{\alpha p}^0={\mathit{b}}_{\mathrm{\Theta }p}^{\mathbf{0}}=0$, μ, λ, γ, estimate an initial image x0.

Loop: set i = 0 and repeat until $\left|\right|{\mathit{x}}^{i+1}-{\mathit{x}}^i|{|}_2<\delta$   ${\mathit{g}}^0={\mathit{z}}^i-\mathit{A}{\mathit{x}}^i$   ${\mathit{d}}^0=-{\mathit{g}}^0$   $k=0$   while   ${\alpha }^k=\frac{{({\mathit{g}}^k)}^{\mathrm{T}}{\mathit{d}}^k}{{({\mathit{d}}^k)}^{\mathrm{T}}\mathit{A}{\mathit{d}}^k}$   ${\mathit{u}}^{k+1}={\mathit{u}}^k+{\alpha }^k{\mathit{d}}^k$   ${\mathit{g}}^{k+1}={\mathit{g}}^k-{\alpha }^k\mathit{A}{\mathit{d}}^k$   if $\left|\right|{\mathit{g}}^{k+1}\left|\right|<\epsilon$, break    ${\beta }^k=\frac{{({\mathit{g}}^{k+1})}^T{\mathit{g}}^{k+1}}{{({\mathit{g}}^k)}^{\mathrm{T}}{\mathit{g}}^k}$   ${\mathit{d}}^{k+1}={\mathit{g}}^{k+1}+{\beta }^k{\mathit{d}}^k$   $k=k+1$   return ${\mathit{u}}^{k+1}$   ${\mathit{x}}^{i+1}={\mathit{u}}^{k+1}$   ${\mathrm{\Theta }}_p^{i+1}=\mathrm{shrink}\left({\mathrm{\Psi }}_p^{3D}{x}^{i+1}+{\mathit{b}}_{\mathrm{\Theta }p}^i,1/\gamma \right)$   ${\mathit{\alpha }}_p^{i+1}=\mathrm{shrink}\left({\mathrm{\Psi }}_p^{2D}{\mathit{x}}^{i+1}+{\mathit{b}}_{\alpha p}^i,1/\lambda \right)$   ${\mathit{b}}_{\alpha p}^{i+1}={\mathit{b}}_{\alpha p}^i+({\mathrm{\Psi }}_p^{2D}{\mathit{x}}^{i+1}-{\mathit{\alpha }}_p^{i+1})$   ${\mathit{b}}_{\mathrm{\Theta }p}^{i+1}={\mathit{b}}_{\mathrm{\Theta }p}^i+({\mathrm{\Psi }}_p^{3D}{\mathit{x}}^{i+1}-{\mathrm{\Theta }}_p^{i+1})$   $i=i+1$

End Loop

Output:x