International Journal of Computer Vision
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Globally Minimal Surfaces by Continuous Maximal Flows
IEEE Transactions on Pattern Analysis and Machine Intelligence
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In this article we study a continuous primal-dual method proposed by Appleton and Talbot and generalize it to other problems in image processing. We interpret it as an Arrow-Hurwicz method which leads to a better description of the system of PDEs obtained. We show existence and uniqueness of solutions and get a convergence result for the denoising problem. Our analysis also yields new a posteriori estimates.