Scientific Interests

I am engaged in research within the fields of image processing, computer vision, and scientific computing, with a primary focus on employing partial differential equations and variational principles. My work involves creating mathematical models and efficient numerical algorithms to address various image-related tasks, such as image restoration, enhancement, compression, and optic flow computation via transport equations.

Currently, my research is centered around another application of the transport equation, namely multiphase reactive transport in porous media. It aims to model the way a substance (such as a gas or a liquid) moves through a porous material (for example rocks or sand) while undergoing chemical reactions.

My doctoral thesis focus on image and video compression using mathematical models based on partial differential equations. It introduces mathematical criteria for determining which pixels should be preserved during image compression, examines optical flow techniques for video compression, and provides a comparative analysis of a novel video codec alongside existing codecs. Additionally, it proposes performance enhancements achieved through GPU computing.

Keywords: Inverse problems, Total Variation, Shape Optimization, Optimal Transport, Inpainting, Multiphase Reactive Transport, Numerical Analysis.