Fast ADMM solver for reweighted total variation image deconvolution and inpainting

Reweighted sparsity approaches are known to be effective and robust for signal reconstruction, yet costly because they require solving an optimization per reweight. In this paper, we consider reweighted total variation (RWTV) as an effective regularization scheme for image deconvolution and inpainting. Motivated to solve this problem efficiently, we build on the alternating directions method of multipliers (ADMM), which is known to be a practical solver for such image inverse problems. We expand on existing ADMM frameworks for deconvolution and inpainting to develop a fast RWTV-ADMM solver framework. In particular, the iterative nature of both the ADMM algorithm and RWTV was exploited to develop an efficient method that integrates the iterations. In addition, we describe a GPU-accelerated implementation of the proposed solver and demonstrate its efficiency for a real-time application in microscopy cell de-convolution and segmentation.