Wideband imaging with the decomposition of time reversal operator

Abstract

It has been shown that the decomposition of the time reversal operator (DORT) is effective to achieve detection and selectively focusing on pointlike scatterers. Moreover, the multiplicity of the invariant of the time reversal operator for a single extended (non-pointlike) scatterer has been also revealed. In this paper, we investigate the characterization and imaging of the scatterers when an extended scatterer and a pointlike scatterer are simultaneously present. The relationship between the quality of focusing and frequency is investigated by backpropagation of singular vectors using a model of the waveguide in each frequency bin. When the extended scatterer is present, it is shown that the second singular vector can also focus on the target. However, the task of focusing can only be achieved in frequency bins with relatively large singular values. When both scatterers are simultaneously present, the singular vectors are a linear combination of the transfer vector from each scatterer. The first singular vector can achieve focusing on the extended scatterer in frequency bins with relatively large singular values. The second singular vector can approximately focus on the pointlike scatterer in frequency bins that its scattering coefficients are relatively high and the first scattering coefficient of the extended scatterer are relatively low.