ABSTRACT
Towards finding the connections between wavelets and the PDE method in image processing, we bring the two subjects closer in this chapter by developing the digital version of the PDE method. Continuous image domains are digitized to graphs and the Euler-Lagrange PDE equations become algebraic ones. Algorithms of these equations connect the digital PDE method to iterations of local digital filters (linear or nonlinear). We develop a self-contained theory of existence and uniqueness of the solutions, which avoids the technical difficulties appearing in classical continuous models and thus makes it easier for general readers without PDE backgrounds to understand and apply it. The PDE method has various applications in image analysis. In this chapter, we focus on denoising and restoration.
