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Award ID contains: 2006881

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  1. ; ; (, Inverse Problems)
    Abstract We develop a linearized boundary control method for the inverse boundary value problem of determining a density in the acoustic wave equation. The objective is to reconstruct an unknown perturbation in a known background density from the linearized Neumann-to-Dirichlet map. A key ingredient in the derivation is a linearized Blagoves̆c̆enskiĭ’s identity with a free parameter. When the linearization is at a constant background density, we derive two reconstructive algorithms with stability estimates based on the boundary control method. When the linearization is at a non-constant background density, we establish an increasing stability estimate for the recovery of the density perturbation. The proposed reconstruction algorithms are implemented and validated with several numerical experiments to demonstrate the feasibility. 
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  2. ; (, SIAM Journal on Applied Mathematics)
    Full Text Available 
  3. (, Notices of the American Mathematical Society)
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  4. (, Notices of the American Mathematical Society)
    This essay provides a glimpse into the extensive landscape of inverse problems within BioLuminescence Tomography. The primary objective is to offer an introduction to this fascinating field and to outline some interesting mathematics in imaging sciences, with the hope of sparking the interest of junior researchers and inspiring their future contributions. 
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    Accepted Manuscript Full Text Available
  5. ; ; (, Communications on Applied Mathematics and Computation)
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  6. ; ; ; (, SIAM Journal on Applied Mathematics)
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  7. ; ; ; (, Biomedical Applications in Molecular, Structural, and Functional Imaging)
    Gimi, Barjor S.; Krol, Andrzej (Ed.)
    Full Text Available 
  8. ; ; (, Inverse Problems)
    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. 
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    Full Text Available 
  9. ; ; ; (, SIAM Journal on Imaging Sciences)
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  10. ; ; (, The Journal of Geometric Analysis)
    null (Ed.)
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