Direct sampling method for monostatic radar imaging

Analysis and Improvement of Direct Sampling Method in the Monostatic Configuration

“…Let us now deal with the monostatic configuration in which an antenna acts as receiver and transmitter, implyingd n = −x n , and is moved from place to place giving a set of measured far-field pattern data defined by M = {u ∞ (x n ,d n ) : n = 1, 2, · · · , N } As examplified in [21], the direct sampling method in such a configuration failed to provide a proper localisation of the defects (see also Fig. 2) when using the indicator function I mono DSM (z) directly deduced from (2) and defined as…”

“…In [21], a modified indicator involving a heuristic factor is proposed to solve the problem, yet no theoretical explanation is provided. In the following the theoretical reason of this miss-localization is exhibited and a modified version of the DSM is introduced.…”

“…We refer to [17,20] for details. Though, a new intuitive indicator function of DSM in the mono-static configuration has already been proposed in [21], no theoretical explanation has been given yet to explain the failure of the classical DSM approach in such a configuration. Recently, in [22], the authors have investigated the mathematical structure of the DSM indicator function in the multistatic configuration using near-field data, proposed an improved version and confirmed its link with the classical Kirchhoff migration technique.…”

Direct Sampling Methods for Inverse Scattering Problems

“…Ito, et al [33] extended the method in [32] for electromagnetic scattering problems. Bektas and Ozdemir [5] extended the use of conventional direct sampling method (DSM), which is only applicable to the multi-static measurement data, to the mono-static measurement data for radar imaging applications. They define a testing function which can be used in the indicator function of DSM with mono-static data.…”

“…5) where ρ = 1 or ρ = 2, fory ∈ R n and fixed k ∈ R + for the fixed frequency case.Numerical examples show that the indicator function µ[M D] is a good indicator for shape reconstruction for extended scatterers. Potthast also extended the indicator function in (2.3) to one-wave multi-frequency situation.…”