Algorithm 2: Target-Preserving Sparse DWT (TPS-DWT)

Input: RD map $X\in R^{\mathit{M}\times \mathit{N}}$; wavelet basis $\psi$; decomposition level $L$; Output: Enhanced RD map $\widehat{\mathit{X}}$.

1:perform L-level 2D Discrete Wavelet Transform:   2: $\{A_L,D_L^H,D_L^V,D_L^D,\dots ,D_1^H,D_1^V,D_1^D\}\leftarrow \mathrm{D}\mathrm{W}\mathrm{T}(X,\psi );$   3:for $\mathrm{l} = 1$ to $\mathrm{L}$ do    4:      for each coefficient $c$ in $\{D_l^H,D_l^V,D_l^D\}$ do   5:             Compute soft threshold;   6:             $c^{\prime }\leftarrow$ sign $(c)\cdot \mathrm{m}\mathrm{a}\mathrm{x}(|c|-\lambda ,0)$;   7:         if $M$ indicates target region at coefficient $c$ then    8:               Keep original coefficient;   9:               $c^{\prime }\leftarrow c$;   10:         end   11:         Update detail coefficient with $c^{\prime }$;   12:      end   13:end    14:Reconstruct enhanced RD map:   15:$\widehat{X}\leftarrow \mathrm{I}\mathrm{D}\mathrm{W}\mathrm{T}(A_L,D_L^{H^{\prime }},D_L^{V^{\prime }},D_L^{D^{\prime }},\dots )$;   16: return $\widehat{X}$