Plane-Wave Detection: a Nonlinearly Ill-Posed Inverse Problem

: It is commonplace that inverse problems of applied mathematics are often ill-posed. Such a problem generally takes the (idealized ) form of a functional equation involving a map 4), representing the physical connection between model and data: phi(x) = z with Z (the model, or solution) and x (the data) ranging over suitable function spaces, on which the map phi is defined.