1,469 research outputs found
Inversion of multiconfiguration complex EMI data with minimum gradient support regularization: A case study
Frequency-domain electromagnetic instruments allow the collection of data in
different configurations, that is, varying the intercoil spacing, the
frequency, and the height above the ground. Their handy size makes these tools
very practical for near-surface characterization in many fields of
applications, for example, precision agriculture, pollution assessments, and
shallow geological investigations. To this end, the inversion of either the
real (in-phase) or the imaginary (quadrature) component of the signal has
already been studied. Furthermore, in many situations, a regularization scheme
retrieving smooth solutions is blindly applied, without taking into account the
prior available knowledge. The present work discusses an algorithm for the
inversion of the complex signal in its entirety, as well as a regularization
method that promotes the sparsity of the reconstructed electrical conductivity
distribution. This regularization strategy incorporates a minimum gradient
support stabilizer into a truncated generalized singular value decomposition
scheme. The results of the implementation of this sparsity-enhancing
regularization at each step of a damped Gauss-Newton inversion algorithm (based
on a nonlinear forward model) are compared with the solutions obtained via a
standard smooth stabilizer. An approach for estimating the depth of
investigation, that is, the maximum depth that can be investigated by a chosen
instrument configuration in a particular experimental setting is also
discussed. The effectiveness and limitations of the whole inversion algorithm
are demonstrated on synthetic and real data sets
Microwave Imaging of 3D Dielectric Structures by Means of a Newton-CG Method in Spaces
An increasing number of practical applications of three-dimensional microwave imaging require accurate and efficient inversion techniques. In this context, a full-wave 3D inverse-scattering method, aimed at characterizing dielectric targets, is described in this paper. In particular, the inversion approach has a Newton-based structure, in which the internal linear solver is a conjugate gradient-like algorithm in lp spaces. The presented results, which include the inversion of both numerical and experimental scattered-field data obtained in the presence of homogeneous and inhomogeneous targets, validate the reconstruction capabilities of the proposed technique
Efficient Inversion of Multiple-Scattering Model for Optical Diffraction Tomography
Optical diffraction tomography relies on solving an inverse scattering
problem governed by the wave equation. Classical reconstruction algorithms are
based on linear approximations of the forward model (Born or Rytov), which
limits their applicability to thin samples with low refractive-index contrasts.
More recent works have shown the benefit of adopting nonlinear models. They
account for multiple scattering and reflections, improving the quality of
reconstruction. To reduce the complexity and memory requirements of these
methods, we derive an explicit formula for the Jacobian matrix of the nonlinear
Lippmann-Schwinger model which lends itself to an efficient evaluation of the
gradient of the data- fidelity term. This allows us to deploy efficient methods
to solve the corresponding inverse problem subject to sparsity constraints
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