The bulk is there:
https://www.researchgate.net/publication/220663968
But it’s heavily modified for a multi-scale wavelet scheme using B-spline cardinal wavelets regularized in variance. Some pointers here:
The base paper only deals with diffusion along isophotes, I have generalized the framework to support diffusion along gradients and isotropic diffusion.
Also, the PDE is solved for each wavelet scale on the high-freq layer (which is more or less equivalent to a laplacian already, by the properties of the B-spline wavelet, so it’s kind of solving a 4th order), and on the low-freq layer (residual).
Each wavelet scale is solved sequentially from coarse to fine to speed-up convergence and avoid local min/max.