How to Solve Image Denoising with Total Variation Prior Using ADMM?
I have done a bit of this myself and you'd need to adapt.
There is a Douglas Rachford self implemented and a primal dual approach here implemented in Recovery of Fusion Frame Structured Signal via Compressed Sensing.
Note that Clarice Poon (Bath University) had some nice tutorials on it.
Another source is the Numerical Tours from Gabriel Peyre. See Denoising by Sobolev and Total Variation Regularization.