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.

Currently, my research is centered around the 'Locally adaptive methods for free discontinuity problems' project. Within this project, I explore topics such as parameter selection, adaptive meshing, numerical methods for partial differential equations, total variation minimization, and the assessment of a posteriori errors.

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, Γ-convergence, Inpainting, Numerical Analysis.