Partial Differential Equation and Variational Methods in Image processing: Introduction and application to biological imaging

We will first introduce the basic concept of partial differential equation (PDE) and variational methods in image processing, including the motivation for the two approaches and their interconnections. We will then talk about our recent work in these two areas with a focus on biological imaging. In image denoising, we present a nonlinear anisotropic diffusion model for denoising images containing blobs and ridges, two of the most prominent features in biological imaging. We will further discuss a variational model for image reconstruction, which includes both image deburring and denoisiong, to achieve super-resolution imaging based on diffraction-limited observations.