We consider the problem of selective imaging extended reflectors in waveguides using the response matrix of the scattered field obtained with an active array. Selective imaging amounts to being able to focus at the edges of a reflector, which typically give rise to weaker echoes than those coming from its main body. To this end, we propose a selective imaging method that uses projections on low-rank subspaces of a weighted modal projection of the array response matrix, P(ω). We analyze theoretically our imaging method for a simplified model problem where the scatterer is a vertical one-dimensional perfect reflector. In this case, we show that the rank of P(ω) equals the size of the reflector divided by the cross-range array resolution. We also derive analytic expressions for the singular vectors of P(ω) and carry out a detailed theoretical analysis of our selective imaging functional. Our numerical simulations are in very good agreement with the theory and illustrate the robustness of our imaging functional for reflectors of various shapes.
We consider the problem of imaging extended reflectors in waveguides using partial-aperture array, i.e. an array that does not span the whole depth of the waveguide. For this imaging, we employ a method that back-propagates a weighted modal projection of the usual array response matrix. The challenge in this setup is to correctly define this projection matrix in order to maintain good energy concentration properties for the imaging method, which were obtained previously by Tsogka et al (2013 SIAM J. Imaging Sci. 6 2714–39) for the full-aperture case. In this paper we propose a way of achieving this and study the properties of the resulting imaging method.
We consider the problem of imaging extended reflectors in terminating waveguides. We form the image by back-propagating the array response matrix projected on the waveguide's non evanescent modes. The projection is adequately defined for any array aperture size covering fully or partially the waveguide's vertical cross-section. We perform a resolution analysis of the imaging method and show that the resolution is determined by the central frequency while the image's signalto-noise ratio improves as the bandwidth increases. The robustness of the imaging method is assessed with fully non-linear scattering data in terminating waveguides with complex geometries.
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