IST - Partial Differential Equations and their Applications to Image Processing (2024)

Venue: IIT, Mandi

Dates: 3 Jun 2024 to 15 Jun 2024

Due to the natural barriers of acquiring equipment or the presence of intermittent fluctuations in the medium, the images acquired by a scanner or digital camera are generally contaminated by different types of noises. Hence, the image restoration is a crucial stage for high-level image analysis. In recent years, PDE based models; specially diffusion models and variational models, have become widely applicable for noise removal and signal reconstruction, due to their well-established mathematical properties and their general wellposedness. It is therefore important to understand the mathematical aspects of PDEs and their solution process. This type of PDE models delas with higher order PDEs, sometimes they are highly non-linear and coupled. Theoretical aspects of these PDE models mainly deals with the existence and uniqueness of the weak solutions by using fixed point theorem. The solution process includes numerical methodologies to find approximate (numerical) solutions.
Proposed instructional school aims to provide the participants a basic understanding of the digital images and relation with PDEs. Through this school, the participants will get a taste of classical theory of second order PDEs and they will be introduced to the advanced PDEs through higher order diffusion equations and variational approach. Furthermore, the school aims to demonstrate numerical techniques, using MATLAB software, to solve several PDE-based mathematical models used in image restoration. The topics in this school are designed in such way that the participants get exposure to topics in both classical and modern approaches in the theory and computation of PDEs and its applications to image processing, which are also part of the curriculum in the universities and post graduate colleges.