Continuous Primal-Dual Methods for Image Processing
Provides theoretical foundations for a class of continuous optimization methods in image processing, but the results are incremental and domain-specific.
The authors generalize a continuous Primal-Dual method to various image processing problems, proving existence, uniqueness, and convergence for denoising, and deriving new a posteriori estimates.
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.