Primal-Dual Plug-and-Play Image Restoration

We propose a new plug-and-play image restoration method based on primal-dual splitting. Existing plug-and-play image restoration methods interpret any off-the-shelf Gaussian denoiser as one step of the so-called alternating direction method of multipliers (ADMM). This makes it possible to exploit the power of such a highly-customized Gaussian denoising method for general image restoration tasks in a plug-and-play fashion. However, the ADMM-based plug-and-play approach (ADMMPnP) has several limitations: 1) it often requires a problem-specific iterative method in solving a subproblem, which results in a computationally expensive inner loop; and 2) it is specialized to handle the formulation of a regularization (plug-and-play) term plus a data-fidelity term, so that it does not allow to impose hard constraints useful for image restoration. Our approach resolves these issues by leveraging the nature of primal-dual splitting, yielding a very flexible plug-and-play image restoration method. Experimental results demonstrate that the proposed method is much more efficient than ADMMPnP with an inner loop, whereas it keeps the same efficiency as ADMMPnP in the case where the subproblem of ADMMPnP can be solved efficiently.