Denoising of image gradients and total generalized variation denoising
This work addresses image denoising for computer vision applications, presenting an incremental improvement by integrating gradient estimates and optimizing computational methods.
The authors tackled image denoising by augmenting total variation with an estimated image gradient, improving reconstruction quality and linking it to total generalized variation denoising, while developing a parameter-free variational model and efficient numerical methods. Numerical experiments showed good denoising properties and significantly increased convergence speed with preconditioning.
We revisit total variation denoising and study an augmented model where we assume that an estimate of the image gradient is available. We show that this increases the image reconstruction quality and derive that the resulting model resembles the total generalized variation denoising method, thus providing a new motivation for this model. Further, we propose to use a constraint denoising model and develop a variational denoising model that is basically parameter free, i.e. all model parameters are estimated directly from the noisy image. Moreover, we use Chambolle-Pock's primal dual method as well as the Douglas-Rachford method for the new models. For the latter one has to solve large discretizations of partial differential equations. We propose to do this in an inexact manner using the preconditioned conjugate gradients method and derive preconditioners for this. Numerical experiments show that the resulting method has good denoising properties and also that preconditioning does increase convergence speed significantly. Finally we analyze the duality gap of different formulations of the TGV denoising problem and derive a simple stopping criterion.