Improved image restoration numerical methods through deep learning

Post by Diogo Lobo

I am currently a PhD Student at the Centre for Mathematics of the University of Coimbra (CMUC). I find that the University of Coimbra provides a vibrant and stimulating environment for research both in Mathematics and Biomedical Sciences, with state of the art technological facilities and internationally recognized research centers. Moreover, it is a city with an intense cultural scene, where one can explore a myriad of artistic endeavors to complement his/her academic interests.

My research focuses mainly on the post-processing of medical imaging, namely Magnetic Resonances (MRIs) and Optical Coherence Tomography’s (OCTs). My aim is the development of mathematical models for noise removal adapted to state of the art medical imaging modalities, namely for data sets where the time factor arises and where the need for motion-coherent post-processing algorithms is crucial.

Image processing methods based on partial differential equations (PDEs) allow for good physical interpretation of the equations, and during the last decades nonlinear diffusion filters have become a powerful and widely investigated tool for such task. In recent years, the machine learning (ML) approach to image processing tasks has surpassed traditional techniques. Namely, the development of neural networks for noise removal and image segmentation achieve impressive performances. However, the lack of theoretical foundations and the black-box nature of these ML algorithms cause some reservations in both research and clinical communities. My strategy is the use of deep learning techniques to determine the optimal parameters for each specific task, and the use of this new found knowledge to create fast, precise and robust numerical methods.

Both the research topic, the proposed mathematical tool set, and the application to medical image data, can be transferred to a broad scope of related problems. Consequently, there are numerous envisaged connections to other research groups within the university and industry and these will be diligently promoted for furthering the impact of the proposed research project.