Digitized PDE method for data restoration (Q2702487)

The wavelet technique and the Partial Differential Equation (PDE) method are efficient tools in image analysis. The PDE method originates in variational models for data denoising and restoration, image segmentation, object detection, etc. Image restoration is typically connected to various types of diffusions. The existing PDE models are mostly the Euler-Lagrange equations for certain energy functionals.NEWLINENEWLINENEWLINEIn this paper, the authors are interested in connections between wavelet technique and PDE method in image processing. They develop a digitized PDE method on graphs. Images are modeled by graphs. The digitized PDE method starts directly with the discrete variational problem, from which algebraic equilibrium equations analogous to the PDEs are established. Algorithms of these algebraic equations connect the digitized PDE method to iterations of local digital filters which can be linear or nonlinear. The authors construct the energy functions and the restoration equations, analyze properties of these equations (such as existence and uniqueness of solutions), design algorithms leading to digital filters, and show numerical results of data denoising and restoration.NEWLINENEWLINEFor the entire collection see [Zbl 0954.65001].