  This paper aims at introducing the concept of time-dependent polarization
tensors (TDPTs) for the wave equation associated to a diametrically small
acoustic inclusion, with constitutive parameters different from those of the
background and size smaller than the operating wavelength. Firstly, the
solution to the Helmholtz equation is considered, and a rigorous systematic
derivation of a complete asymptotic expansion of the scattered field due to the
presence of the inclusion is presented. Then, by applying the Fourier
transform, the corresponding time-domain expansion is readily obtained after
truncating the high frequencies. The new concept of TDPTs is shown to be
promising for performing imaging. Numerical simulations are driven, showing
that the TDPTs reconstructed from noisy measurements allow to image fine shape
details of the inclusion.
