I'm guiding a student project to handle texture smoothing, hence I need an alternative to PCG solver which is as existing solver... If you have Matlab code available, could you share it with me?
Try using a multi-grid method, if certain frequency of the solution space is easier to solved at lower resolution, that made a big speed up (in the order of 10-1000) for me when I needed to solve an elliptical partial differential equation.
Here is a wiki link: https://en.wikipedia.org/wiki/Multigrid_method
The good thing about using a multi-grid method is that you could just take an existing iterative solver, and write a loop through different resolution scale.