This is the second volume of a new series of lecture notes of the Abdus Salam International Centre for Theoretical Physics. These new lecture notes are put onto the web pages of the ICTP to allow people from all over the world to access them freely. In addition a limited number of hard copies is printed to be distributed to scientists and institutions which otherwise do not have access to the web pages. This volume contains the lecture notes given by A. Chambolle during the School on Mathematical Problems in Image Processing that took place at the Abdus Salam International Centre for Theoretical Physics from 4 to 22 September 2000 under the direction of L. Ambrosio (Scuola Normale Superiore di Pisa), G. Dal Maso (Scuola Internazionale Superiore di Studi Avanzati) and J.-M. Morel (Ecole Normale Superieure, Cachan). The topic of Chambolle's course was "Inverse problems in image processing and image segmentation: some mathematical and numerical aspects". (ISBN 92-95003-04-7)