2,047 research outputs found
Viscoelastic modulus reconstruction using time harmonic vibrations
This paper presents a new iterative reconstruction method to provide
high-resolution images of shear modulus and viscosity via the internal
measurement of displacement fields in tissues. To solve the inverse problem, we
compute the Fr\'echet derivatives of the least-squares discrepancy functional
with respect to the shear modulus and shear viscosity. The proposed iterative
reconstruction method using this Fr\'echet derivative does not require any
differentiation of the displacement data for the full isotropic linearly
viscoelastic model, whereas the standard reconstruction methods require at
least double differentiation. Because the minimization problem is ill-posed and
highly nonlinear, this adjoint-based optimization method needs a very
well-matched initial guess. We find a good initial guess. For a well-matched
initial guess, numerical experiments show that the proposed method considerably
improves the quality of the reconstructed viscoelastic images.Comment: 15 page
Electrical impedance spectroscopy-based nondestructive testing for imaging defects in concrete structures
An electrical impedance spectroscopy-based nondestructive testing (NDT)
method is proposed to image both cracks and reinforcing bars in concrete
structures. The method utilizes the frequency-dependent behavior of thin
insulating cracks: low-frequency electrical currents are blocked by insulating
cracks, whereas high-frequency currents can pass through the conducting bars
without being blocked by thin cracks. Rigorous mathematical analysis relates
the geometric structures of the cracks and bars to the frequency-dependent
Neumann-to-Dirichlet data. Various numerical simulations support the
feasibility of the proposed method
The Linearized Inverse Problem in Multifrequency Electrical Impedance Tomography
This paper provides an analysis of the linearized inverse problem in
multifrequency electrical impedance tomography. We consider an isotropic
conductivity distribution with a finite number of unknown inclusions with
different frequency dependence, as is often seen in biological tissues. We
discuss reconstruction methods for both fully known and partially known
spectral profiles, and demonstrate in the latter case the successful employment
of difference imaging. We also study the reconstruction with an imperfectly
known boundary, and show that the multifrequency approach can eliminate
modeling errors and recover almost all inclusions. In addition, we develop an
efficient group sparse recovery algorithm for the robust solution of related
linear inverse problems. Several numerical simulations are presented to
illustrate and validate the approach.Comment: 25 pp, 11 figure
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