Multimedia contents are deeply intertwined with our lives, and, as a consequence, they've become an invaluable asset also for investigative and evidentiary use. However, there are still numerous open challenges for law enforcement agencies when it comes to acquire, authenticate, enhance, and analyze images and videos for forensic use. 

The intent of this webinar is to demonstrate the optimality of splines for the resolution of inverse problems in imaging and the design of deep neural networks. To that end, I first present a representer theorem that states that the extremal points of a broad class of linear inverse problems with a generalized total-variation constraint are adaptive splines whose type is linked to the underlying regularization operator.