Given a convex function, there are a lot of methods that could be used to do the optimization, such as gradient decent, CG, primal dual method, PPA, Bregman Iteration, etc. But I am not clear that if there is a method which works in wavelet domain. If anyone knows something about it, please let me know. If you are interested by the topic, you can contact me by email, [email protected], and we can work on it together.