The propagating frame: A novel framework for wave tracking through rough medium and for inverse scattering

We present a novel strategy for tracking wavefields in weakly fluctuating media. Using frame theory, we expand the aperture sources using a windowed Fourier transform frame, expressing the field as beams emerging from a discrete set of exit points and directions in the source domain. We show that, extending the frame concept into the propagation domain, the beams themselves constitute a frame, denoted the propagating frame. In this paper we show that the forward and backward propagating frames provide a full alternative to the conventional plane wave spectrum. We consider the simple problem of radiation from a volume source distribution and show that the beam expansion is obtained by projecting the source onto the propagators in the beam domain, an extension to the conventional plane-wave (Fourier) analysis. The propagating frame representation provides a new self-consistent framework for wave tracking through rough media, where the interaction of the propagating beams with the medium heterogeneities is analyzed locally, and then projected onto the same beam set. Applications for wave tracking through random medium and for inverse scattering will be presented.