On the well-posedness of solution in the inverse scattering problem

The well-posedness, i.e. the existence, uniqueness, and stability of the solution in the inverse scattering problem, is discussed. In addition, the relations between these three aspects of well-posedness are described. The conclusions are that: (i) if the scattered field is measured with errors, then the original operator equation must be replaced by a specific approximate operator equation for the sake of existence; (ii) if a continuous source is replaced approximately by a set of discrete sources, then the nonuniqueness can be overcome; and (iii) the well-posedness depends on the selection of the sample points for measuring the scattered fields. Based on this discussion, rules for selecting the sample points are given. Specifically, it is shown that the sample points in a conical region with a +or-45 degrees angle around the forward direction are more important than those in other regions.<>