Duality for Inverse Problems in Wave Propagation

A general dual formulation for inequality constrained optimization problems applies directly to inverse problems for multi-experiment data fitting. In the case of inverse problems in wave propagation, proper choice of the multi-experiment consistency constraint yields a dual problem with better convexity properties than the “primal” or straightforward data fitting formulation. The plane wave detection problem, a very simple inverse problem in wave propagation, provides a transparent framework in which to illustrate these ideas.