In the last forty years, medical imaging has become of paramount importance in daily clinical practice. Different techniques have been developed in order to capture salient aspects of pathologies and, as scanners and devices became wide-spread available in many hospitals and care facilities, the quantity of data increased dramatically as well.

Regardless of the physics beyond the measurement devices used to acquire the data, images are often richer in content than they appear at first glance. For this reason, many computational approaches have been developed to fully exploit medical imaging data, with the aim to improve treatment of diseases and to help physicians in their clinical choices. 

In this talk I will present an overview of computational methods, belonging to approximation theory, machine learning and inverse problems, for the reconstruction, processing and analysis of medical data.