Algorithm 2: (Variable Exponent Functional Retinex)

Input: Image $I$ Transform into log domain $i=\log (I+1)$; Initialization: $l_{}^0=i$, $b^0=0$, $t^0=0$ and $k=0$ While $\frac{||l^k-l_{}^{k-1}||}{||l_{}^k||}\le \epsilon$   (1) Given $b^k$ and $t^k$, update $l_{}^{k+1}$ by solving Equation (8).   (2)Given $l_{}^{k+1}$ and $t_{}^k$, update $b_{}^{k+1}$ by using algorithm 1.   (3)Update $t^{k+1}=t^k+\nabla l^{k+1}-b^{k+1}$.   (4) $l_{}^{k+1}=\max \{l_{}^{k+1},i\}$;   (5)$k=k+1$; End Output: Image $R=\frac{\exp (i)}{\exp (l)}$