Acceleration of the PDHGM on strongly convex subspaces

We propose several variants of the primal-dual method due to Chambolle and Pock. Without requiring full strong convexity of the objective functions, our methods are accelerated on subspaces with strong convexity. This yields mixed rates, O (1/N 2) with respect to initialisation andO (1/N ) with respect to the dual sequence, and the residual part of the primal sequence. We demonstrate the e cacy of the proposed methods on image processing problems lacking strong convexity, such as total generalised variation denoising and total variation deblurring.