Reduced order model approach for imaging with waves

Abstract

We introduce a novel, computationally inexpensive approach for imaging with an active array of sensors, which probe an unknown medium with a pulse and measure the resulting waves. The imaging function uses a data driven estimate of the "internal wave" originating from the vicinity of the imaging point and propagating to the sensors through the unknown medium. We explain how this estimate can be obtained using a reduced order model (ROM) for the wave propagation. We analyze the imaging function, connect it to the time reversal process and describe how its resolution depends on the aperture of the array, the bandwidth of the probing pulse and the medium through which the waves propagate. We also show how the internal wave can be used for selective focusing of waves at points in the imaging region. This can be implemented experimentally and can be used for pixel scanning imaging. We assess the performance of the imaging methods with numerical simulations and compare them to the conventional reverse-time migration method and the "backprojection" method introduced recently as an application of the same ROM.

References in corpus (7)

• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• Direct, nonlinear inversion algorithm for hyperbolic problems via projection-based model reduction
• Untangling the nonlinearity in inverse scattering with data-driven reduced order models
• A nonlinear method for imaging with acoustic waves via reduced order model backprojection
• Lippmann-Schwinger-Lanczos algorithm for inverse scattering problems
• Robust nonlinear processing of active array data in inverse scattering via truncated reduced order models
• Reduced order models for spectral domain inversion: Embedding into the continuous problem and generation of internal data