Block Decomposition Methods for Total Variation by Primal-Dual Stitching

Abstract

Due to the advance of image capturing devices, huge size of images are available in our daily life. As a consequence the processing of large scale image data is highly demanded. Since the total variation (TV) is kind of de facto standard in image processing, we consider block decomposition methods for TV based variational models to handle large scale images. Unfortunately, TV is non-separable and non-smooth and it thus is challenging to solve TV based variational models in a block decomposition. In this paper, we introduce a primal-dual stitching (PDS) method to efficiently process the TV based variational models in the block decomposition framework. To characterize TV in the block decomposition framework, we only focus on the proximal map of TV function. Empirically, we have observed that the proposed PDS based block decomposition framework outperforms other state-of-art methods such as Bregman operator splitting based approach in terms of computational speed