The linear sampling method in a lossy background: an energy perspective

In this article we propose a physical approach to the linear sampling method (LSM) for a possibly inhomogeneous and lossy background, whereby the modified far-field equation at the basis of the method can be regarded as a constraint on the power fluxes carried by the Poynting vector associated with the scattered field. Under appropriate assumptions on the flow lines of this Poynting vector, the general theorem inspiring the LSM (and concerning the existence of approximate solutions to the modified far-field equation) can be reformulated in a different way, which is more appropriate to explain the performance of the method.