: In this talk we give a snapshot of our research on complex diffusion processes considering applications in image processing. In particular, we present an adaptive complex diffusion filter to improve the process of speckle noise reduction in optical coherence tomograms from the human retina. Optical coherence tomography (OCT) is a non-invasive imaging modality with an increasing number of applications and it is becoming an essential tool in ophthalmology allowing in vivo high-resolution cross-sectional imaging of the retinal tissue. However, as any imaging technique that bases its image formation on coherent waves, OCT images suffer from speckle noise, which reduces its quality.

The main focus of our work is on implicit-explicit finite difference schemes for complex diffusion filtering. These numerical methods are studied according to their quantitative and qualitative characteristics. Some numerical results are presented in the context of a collaboration with the Institute of Biomedical Research in Light and Image (IBILI), a research institution of the Faculty of Medicine of the University of Coimbra.

Joint work with Rui Bernardes, Cristina Maduro, Pedro Serranho, Sílvia Barbeiro, José Cunha-Vaz.
