Analysis of new direct sampling indicators for far-field measurements

This article focuses on the analysis of three direct sampling indicators which can be used for recovering scatterers from the far-field pattern of time-harmonic acoustic measurements. These methods fall under the category of sampling methods where an indicator function is constructed using the far-field operator. Motivated by some recent work, we study the standard indicator using the far-field operator and two indicators derived from the factorization method. We show the equivalence of two indicators previously studied as well as propose a new indicator based on the Tikhonov regularization applied to the far-field equation for the factorization method. Finally, we give some numerical examples to show how the reconstructions compare to other direct sampling methods

Object Identification in Radar Imaging via the Reciprocity Gap Method

In this paper, we present an experimental method for locating and identifying objects in radar imaging, specifically problems that could arise in physical situations. The data for the forward problem are generated using a discretization of the Lippmann‐Schwinger equation, and the inverse problem of object location is solved using the reciprocity gap approach to the linear sampling method. The main new development in this paper is an exploration of determining the permittivity of the object from the back‐scattered data, utilizing another discretization of the Lippmann‐Schwinger equation. Abstract © AGU