Algorithm 1. Proposed DSC-THz Imaging Algorithm

Input: measurement y, measurement matrix R, exponential shift invariant wavelet basis We, horizontal gradient operator $T_x$, vertical gradient operator $T_y$. Initialization: ${\mathit{x}}^0={\mathit{R}}^{-1}\mathit{y}$,${\mathit{r}}_e^0={\mathit{d}}_x^0={\mathit{d}}_y^0={\mathit{b}}_r^0={\mathit{b}}_x^0={\mathit{b}}_y^0=0$,$\mu$,$\lambda$,$\gamma$ Loop: set $i=0$ and repeat until ($||{\mathit{x}}^{i+1}-{\mathit{x}}^i|{|}_2<\delta$)   ${\mathit{x}}^{i+1}={\left(\mu {\mathbf{R}}^{\mathrm{T}}\mathbf{R}+\gamma T_x^T{T}_x+\gamma T_y^T{T}_y+\lambda \mathbf{I}\right)}^{-1}{\mathit{z}}^i$   ${\mathit{r}}_e^{i+1}=\mathrm{shrink}\left(W_e{\mathit{x}}^{i+1}+{\mathit{b}}_r^i,1/\lambda \right)$   ${\mathit{d}}_x^{i+1}=\mathrm{shrink}\left(T_x{\mathit{x}}^{i+1}+{\mathit{b}}_x^i,1/\gamma \right)$   ${\mathit{d}}_y^{i+1}=\mathrm{shrink}\left(T_y{\mathit{x}}^{i+1}+{\mathit{b}}_y^i,1/\gamma \right)$   ${\mathit{b}}_r^{i+1}={\mathit{b}}_r^i+(W_e{\mathit{x}}^{i+1}-{\mathit{r}}_e^{i+1})$   ${\mathit{b}}_x^{i+1}={\mathit{b}}_x^i+(T_x{\mathit{x}}^{i+1}-{\mathit{d}}_x^{i+1})$   ${\mathit{b}}_y^{i+1}={\mathit{b}}_y^i+(T_y{\mathit{x}}^{i+1}-{\mathit{d}}_y^{i+1})$   $i=i+1$ End loop Output: reconstructed terahertz image x.