Thank you for this meaningful repository and I wonder if the following code
rhs = y - rho*Dt(y1/rho + v1, y2/rho + v2);
should be corrected to
rhs = y - rho*Dt(y1/rho - v1, y2/rho - v2);
(ADMM Image Denoising/ADMM.m)
according to
$$argmin_{x,y,u}\frac{1}{2}{|x-y|_2^2+\lambda|v_1|_1+\lambda|v_2|_1+y_1^T(D_xx-v_1)+\frac{\rho}{2}(D_xx-v_1)_2^2+y_2^T(D_yx-v_2)+\frac{\rho}{2}(D_yx-v_2)_2^2}$$
$$\Rightarrow x: (x-y)+\rho D_x^T(D_xx-v_1+\frac{y_1}{\rho})+\rho D_y^T(D_yx-v_2+\frac{y_2}{\rho})=0$$
$$\Rightarrow x=(I+\rho D_x^TD_x+\rho D_y^TD_y)^{-1}(y+\rho D_x^T(v_1-\frac{y_1}{\rho})+\rho D_y^T(v_2-\frac{y_2}{\rho}))$$
From my tests, results could get improved after this correction.