Some Remarks on Time-Reversal MUSIC for Two-Dimensional Thin PEC Scatterers

Time-reversal MUSIC is a super-resolving imaging method that allows localizing point-like scatterers with a resolution much smaller than the diffraction limits. In this letter, we check this statement for a populated scattering scene for the case of 2-D cylindrical perfect electric conducting objects. It is shown that when the data are corrupted even by a small amount of noise, there is an intrinsic limit on the number of scatterers that can be successfully detected. This number turns out to be linked with the so-called number of degrees of freedom corresponding to the spatial region where the targets are located. Moreover, it is shown that the transverse electric polarization is more sensitive to the noise as, given the size of the spatial region occupied by the scatterers, the maximum number of scatterers that can be detected is three times lower than that detectable by the transverse magnetic illumination.