Back-propagation imaging by exploiting multipath from point scatterers

An inverse scattering problem under the linearised Born approximation is considered for a non-homogeneous background medium. An ensemble of pointlike scatterers is oppositely deployed in the scattering scene in order to introduce multipath and to gain an advantage in the reconstruction procedure. It is well known that inverse scattering can benefit from multipath, but at the same time it can produce artefacts in the reconstructions. This is confirmed once again in this study. Indeed, we show that some artefacts, which have been discarded in some previous works, are actually the cause of resolution improvement. To this end, standard stationary phase arguments are employed along with an adjoint inversion method (backpropagation). Theoretical results succeeds in predicting the reconstruction's leading order terms. However, spurious artefacts due to high order terms become relevant, because more than one point scatterer is used. A simple way to mitigate such artefacts without renouncing the gain in resolution is introduced for the case where the unknown scatterers are small compared to the wavelength.