Francois Lauze
Total variation in Image Analysis.
Since the classical work of Rudin, Osher and Fatemi, total variation has been used in numerous problems. Tichonov quadratic like regularizer cannot preserve edges, I will provide an explanation behind this phenomenon, this leads naturally to the introduction of Total Variation. In this short course, I will provide a a precise definition of total variation, some of its properties and discuss its minimization in a series of problems ranging from image denoising to image compression as well as possible implementations and discuss links with sparsity in imaging.