Inverse Problems with Constraints

Many design questions in telecommunications, signal processing and control can be formulated as inverse problems. Moreover, there is a surprising degree of similarity in the solutions to the problems from diverse areas. Here we will outline some basic approaches to solving inverse problems and draw connections between different areas of application. Inverse problems become particularly interesting (and difficult) when the solution is required to satisfy hard and/or soft constraints. Recent research results on this topic will be outlined and the impact on practical problems discussed.