Dual Formulation of the TV-Stokes Denoising Model for Multidimensional Vectorial Images

The TV-Stokes denoising model for a vectorial image defines a denoised vector field in the form of the gradient of a scalar function. The dual formulation naturally leads to a Chambolle-type algorithm, where the most time consuming part is application of the orthogonal projector onto the range space of the gradient operator. This application can be efficiently executed by the fast cosine transform taking advantage of the fast Fourier transform. Convergence of the Chambolle-type iteration can be improved by Nesterov’s acceleration.