Algorithm 1  Multi-scale fusion and denoising of NIR and RGB images.

Input: Noisy gray image from RGB image, NIR image Initialize: ${\mathit{\omega }}_1={\mathit{\omega }}_2=0.5$,${\mathit{\sigma }}_1=0.5$,${\mathit{\gamma }}_1=2$, $\mathit{\eta }=0.005$ $\mathit{\beta }=1.2$, $\mathit{\epsilon }=0.001$, ${\mathit{\alpha }}^0=\mathit{I}$, ${\mathit{v}}^0=\mathit{u}$ $M=3\sim 5$, $N=20$, $\mathit{\tau }={10}^{-4}$, ${\mathit{\epsilon }}_1={\mathit{\epsilon }}_2={10}^{-2}$. 1. Perform DT-CWT on noisy gray and NIR images. 2. Detail layer: For m=1:M (M: Maximum decomposition)     For n=1:N (N: Maximum iteration number)         a. Calculate $VI$ of ${\mathit{v}}^n$ and $\mathit{g}$ [24];         b. Calculate ${\mathit{\alpha }}_{\mathbf{0}}$ from $\mathit{g}$ by (13);         c. Calculate ${\mathit{\omega }}_{\mathbf{3}}-{\mathit{\omega }}_{\mathbf{5}}$ by (14)–(17);         d. Optimize ${\mathit{\alpha }}^{n+1}$ by (21);         e. Optimize ${\mathit{v}}^{n+1}$ by (23);         if $\parallel {\mathit{\alpha }}^{n+1}-{\mathit{\alpha }}^n{\parallel }_2^2/{\parallel {\mathit{\alpha }}^n\parallel }_2^2<{\mathit{\epsilon }}_1$ and             $\parallel {\mathit{v}}^{n+1}-{\mathit{v}}^n{\parallel }_2^2/{\parallel {\mathit{v}}^n\parallel }_2^2<{\mathit{\epsilon }}_2$; break;      end For  end For 3. Base layer: For n=1:N (N: Maximum iteration number)     a. Calculate $VI$ of ${\mathit{v}}_{\mathit{l}}^{\mathit{n}}$ and ${\mathit{g}}_{\mathit{l}}$ [24];     b. Calculate ${\mathit{\alpha }}_{\mathit{l}\mathbf{0}}$ from g by (26);     c. Calculate ${\mathit{\omega }}_{\mathbf{3}}$ by (14);     d. Optimize ${\mathit{\alpha }}_l^{n+1}$ and ${\mathit{v}}_l^{n+1}$ by (24)–(25);     if $\parallel {\mathit{\alpha }}_{\mathit{l}}^{n+1}-{\mathit{\alpha }}_{\mathit{l}}^n{\parallel }_2^2/{\parallel {\mathit{\alpha }}_{\mathit{l}}^n\parallel }_2^2<{\mathit{\epsilon }}_1$ and         $\parallel {\mathit{v}}_{\mathit{l}}^{n+1}-{\mathit{v}}_{\mathit{l}}^n{\parallel }_2^2/{\parallel {\mathit{v}}_{\mathit{l}}^n\parallel }_2^2<{\mathit{\epsilon }}_2$; break; end For 4. Perform inverse DT-CWT. Output: Fused gray image.