To speed the convergence of the inversion, we can reformulate the inversion problem as a Regularized Inversion with model Preconditioning (RIP) through the use of a preconditioning operator 43#43. This operator should be as close to the inverse of the regularization operator as possible so that 44#44.By mapping the multi-dimensional regularization operator 39#39 to helical space and applying polynomial division, we can apply the exact inverse so that 45#45 (). We also use the preconditioning transformation 46#46 (). My objective function then becomes:
In fitting goals this is:
Now the model styling goal contains the identity operator 49#49, which is very well conditioned. This will allow the iterative inversion to converge faster.