1,913 research outputs found
Regularization strategy for the layered inversion of airborne TEM data: application to VTEM data acquired over the basin of Franceville (Gabon)
Airborne transient electromagnetic (TEM) is a cost-effective method to image
the distribution of electrical conductivity in the ground. We consider layered
earth inversion to interpret large data sets of hundreds of kilometre.
Different strategies can be used to solve this inverse problem. This consists
in managing the a priori information to avoid the mathematical instability and
provide the most plausible model of conductivity in depth. In order to obtain
fast and realistic inversion program, we tested three kinds of regularization:
two are based on standard Tikhonov procedure which consist in minimizing not
only the data misfit function but a balanced optimization function with
additional terms constraining the lateral and the vertical smoothness of the
conductivity; another kind of regularization is based on reducing the condition
number of the kernel by changing the layout of layers before minimizing the
data misfit function. Finally, in order to get a more realistic distribution of
conductivity, notably by removing negative conductivity values, we suggest an
additional recursive filter based upon the inversion of the logarithm of the
conductivity. All these methods are tested on synthetic and real data sets.
Synthetic data have been calculated by 2.5D modelling; they are used to
demonstrate that these methods provide equivalent quality in terms of data
misfit and accuracy of the resulting image; the limit essentially comes on
special targets with sharp 2D geometries. The real data case is from
Helicopter-borne TEM data acquired in the basin of Franceville (Gabon) where
borehole conductivity loggings are used to show the good accuracy of the
inverted models in most areas, and some biased depths in areas where strong
lateral changes may occur
A multiscattering series for impedance tomography in layered media
We introduce an inversion algorithm for tomographic images of layered media. The algorithm is based on a multiscattering series expansion of the Green function that, unlike the Born series, converges unconditionally. Our inversion algorithm obtains images of the medium that improves iteratively as we use more and more terms in the multiscattering series. We present the derivation of the multiscattering series, formulate the inversion algorithm and demonstrate its performance through numerical experiments
An Iterative Procedure for Combining the Advantages of a Multi-Frequency and Multi-Resolution Inversion Algorithm
Starting from the iterative multi�]scaling approach previously studied for monochromatic illuminations, two multi�]resolution strategies for dealing with multi�]frequency inverse scattering experiments have been developed. The first procedure is based on the integration of the iterative multi�]scaling algorithm into a frequency�]hopping reconstruction scheme, while in the second one the multi�]frequency data are simultaneously processed exploiting a multi�]resolution expansion of the problem unknowns. The numerical and the experimental analysis presented in this contribution concern with a preliminary assessment of the reconstruction effectiveness of the proposed approaches in comparison with a monochromatic multi�]step process. This is the author's version of the final version available at IEEE
On Algorithms Based on Joint Estimation of Currents and Contrast in Microwave Tomography
This paper deals with improvements to the contrast source inversion method
which is widely used in microwave tomography. First, the method is reviewed and
weaknesses of both the criterion form and the optimization strategy are
underlined. Then, two new algorithms are proposed. Both of them are based on
the same criterion, similar but more robust than the one used in contrast
source inversion. The first technique keeps the main characteristics of the
contrast source inversion optimization scheme but is based on a better
exploitation of the conjugate gradient algorithm. The second technique is based
on a preconditioned conjugate gradient algorithm and performs simultaneous
updates of sets of unknowns that are normally processed sequentially. Both
techniques are shown to be more efficient than original contrast source
inversion.Comment: 12 pages, 12 figures, 5 table
3D microwave tomography with huber regularization applied to realistic numerical breast phantoms
Quantitative active microwave imaging for breast cancer screening and therapy monitoring applications requires adequate reconstruction algorithms, in particular with regard to the nonlinearity and ill-posedness of the inverse problem. We employ a fully vectorial three-dimensional nonlinear inversion algorithm for reconstructing complex permittivity profiles from multi-view single-frequency scattered field data, which is based on a Gauss-Newton optimization of a regularized cost function. We tested it before with various types of regularizing functions for piecewise-constant objects from Institut Fresnel and with a quadratic smoothing function for a realistic numerical breast phantom. In the present paper we adopt a cost function that includes a Huber function in its regularization term, relying on a Markov Random Field approach. The Huber function favors spatial smoothing within homogeneous regions while preserving discontinuities between contrasted tissues. We illustrate the technique with 3D reconstructions from synthetic data at 2GHz for realistic numerical breast phantoms from the University of Wisconsin-Madison UWCEM online repository: we compare Huber regularization with a multiplicative smoothing regularization and show reconstructions for various positions of a tumor, for multiple tumors and for different tumor sizes, from a sparse and from a denser data configuration
Application of the inhomogeneous Lippmann-Schwinger equation to inverse scattering problems
In this paper we present a hybrid approach to numerically solve
two-dimensional electromagnetic inverse scattering problems, whereby the
unknown scatterer is hosted by a possibly inhomogeneous background. The
approach is `hybrid' in that it merges a qualitative and a quantitative method
to optimize the way of exploiting the a priori information on the background
within the inversion procedure, thus improving the quality of the
reconstruction and reducing the data amount necessary for a satisfactory
result. In the qualitative step, this a priori knowledge is utilized to
implement the linear sampling method in its near-field formulation for an
inhomogeneous background, in order to identify the region where the scatterer
is located. On the other hand, the same a priori information is also encoded in
the quantitative step by extending and applying the contrast source inversion
method to what we call the `inhomogeneous Lippmann-Schwinger equation': the
latter is a generalization of the classical Lippmann-Schwinger equation to the
case of an inhomogeneous background, and in our paper is deduced from the
differential formulation of the direct scattering problem to provide the
reconstruction algorithm with an appropriate theoretical basis. Then, the point
values of the refractive index are computed only in the region identified by
the linear sampling method at the previous step. The effectiveness of this
hybrid approach is supported by numerical simulations presented at the end of
the paper.Comment: accepted in SIAM Journal on Applied Mathematic
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