Search for: All records

Abstract We develop a linearized boundary control method for the inverse boundary value problem of determining a potential in the acoustic wave equation from the Neumann-to-Dirichlet map. When the linearization is at the zero potential, we derive a reconstruction formula based on the boundary control method and prove that it is of Lipschitz-type stability. When the linearization is at a nonzero potential, we prove that the problem is of Hölder-type stability in two and higher dimensions. The proposed reconstruction formula is implemented and evaluated using several numerical experiments to validate its feasibility. 

We consider the problem of velocity inversion/calibration in passive survey, where the seismic source is also an unknown. In earthquake detection or microseismic localization, the major task is to reconstruct the passive seismic sources, but due to the source-velocity coupling, source reconstructions are inherently affected by inaccurate knowledge of the velocity, bringing the need of velocity calibration. We propose a source independent velocity calibration method that recovers the velocity without the source information, thus providing a better ground for source inversion. Unlike existing methods that assume sources to be a linear combination of separated point sources, the proposed method allows sources to lie on a line singularity (representing rock cracks), as long as the activation time is relatively brief. The proposed approach is based on the observation that the spatial distribution of the source is separable from the velocity model after a proper Helmholtz domain projection. 

Photo-Acoustic Tomography (PAT) is an emerging non-invasive hybrid modality driven by a constant yearning for superior imaging performance. The image quality, however, hinges on the acoustic reflection, which may compromise the diagnostic performance. To address this challenge, we propose to incorporate a deep neural network into conventional iterative algorithms to accelerate and improve the correction of reflection artifacts. Based on the simulated PAT dataset from computed tomography (CT) scans, this network-accelerated reconstruction approach is shown to outperform two state-of-the-art iterative algorithms in terms of the peak signal-to-noise ratio (PSNR) and the structural similarity (SSIM) in the presence of noise. The proposed network also demonstrates considerably higher computational efficiency than conventional iterative algorithms, which are time-consuming and cumbersome.