An image decomposition model using the total variation and the infinity Laplacian

This paper is devoted to a recent topic in image analysis: the decomposition of an image into a cartoon or geometric part, and an oscillatory or texture part. Here, we propose a practical solution to the (BV,G) model proposed by Y. Meyer . We impose that the cartoon is a function of bounded variation, while the texture is represented as the Laplacian of some function whose gradient belongs to L∞. The problem thus becomes related with the absolutely minimizing Lipschitz extensions and the infinity Laplacian. Experimental results for image denoising and cartoon + texture separation, together with details of the algorithm, are also presented.