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A method for microwave imaging of dielectric targets is proposed. It is based on a tomographic approach in which the field scattered by an unknown target (and collected in a proper observation domain) is inverted by using an inexact-Newton method developed in

The regularization of ill-posed problems in

The mathematical formulation of the proposed approach is described in the following with reference to transverse-magnetic illumination conditions. The capabilities and limitations of the proposed extended method are evaluated by means of numerical simulations concerning targets in noisy environments for which the forward problem is solved by using the method of moments. The inverse solution is obtained, as mentioned, by using a two-loop inexact-Newton method, which has been developed in the framework of

The paper is organized as follows. The mathematical formulation of the developed approach is discussed in Section

Let us consider the configuration shown in Figure

Configuration of the electromagnetic inverse scattering problem and representation of the measurement setup.

For the sake of simplicity, in the following a single view case is described. Moreover, the

Combining (

By applying (

The inverse problem that must be solved in order to retrieve the dielectric properties of the targets consists in finding the unknown

The reconstruction method is thus composed by the following steps (Newton iterations are denoted by the index

Start the algorithm with an initial guess

Compute the Newton linearization of the operator

Find a function

where

with

The Landweber steps (

Update the solution with the increment

Iterate Newton steps

An important remark has to be devoted to the Fréchet derivative

In (

The proposed multifrequency imaging method in

The scattered field data are computed by a numerical code based on the method of moments [

The object under test has been illuminated by means of electromagnetic fields at three different frequencies:

In order to analyze the method’s performance in different operating conditions, numerical simulations with

Reconstructed distributions of the relative dielectric permittivity of the investigation domain in different operating conditions, with

For comparison purposes, the results provided by a standard inexact-Newton method working in Hilbert spaces [

The graphs in Figure

Reconstructed distributions of the relative dielectric permittivity of the investigation domain in different operating conditions, with

In Figure

Reconstructed distributions of the relative dielectric permittivity of the investigation domain in different operating conditions, with

The inversion results have been quantitatively evaluated using the following relative reconstruction error on the whole investigation domain

Relative reconstruction error on the investigation domain versus the

Relative reconstruction error on the investigation domain versus the

In this case, too, we can observe that on one hand the reconstruction error decreases with an increase in the number of considered frequencies; on the other hand, the use of a Banach space norm leads to significant improvements especially with a reduced number of views

In this paper, a previously developed approach to microwave imaging has been extended to deal with multifrequency processing in free space. The proposed technique is based on an inexact-Newton method and is aimed at inspecting inhomogeneous dielectric cylinders of arbitrary shapes under transverse-magnetic illumination conditions. The use of the inexact-Newton method (modified to take profit of the features of

The authors declare that there are no competing interests regarding the publication of this paper.

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