Lorenzo Crocco

A FEASIBILITY STUDY ON MICROWAVE IMAGING FOR BRAIN STROKE MONITORING

The adoption of microwave imaging as a tool for non- invasive monitoring of brain stroke has recently gained increasing attention. In this respect, the paper aims at providing a twofold contribution. First, we introduce a simple design tool to devise guidelines to properly set the working frequency as well as to choose the optimum matching medium needed to facilitate the penetration of the probing wave into the head. Second, we propose an imaging strategy based on a modifled formulation of the linear sampling method, which allows a quasi real time monitoring of the diseases evolution. The accuracy of the design guidelines and performance of the imaging strategy are assessed through numerical examples dealing with 2D anthropomorphic phantoms.

Subsurface inverse scattering problems: quantifying, qualifying, and achieving the available information

In inverse scattering problems, only a limited amount of independent data is actually available whenever the finite accuracy of the measurement set up is taken into account. In this paper, we deal with the problem of quantifying such an amount in the subsurface sensing case. In particular, an alternative formulation of the problem is given which also allows to understand how to dimensionate the measurement setup in an optimal fashion. Analytical results are reported for the case of a lossless soil, while a numerical study is carried out in the general case. By relying on the same formulation and tools, we also discuss the kind of unknown profiles that can actually be retrieved. In particular, it is shown that the class of retrievable functions exhibits intrinsic multiresolution features. This suggests that adoption of wavelet expansions to represent the unknown function may enhance the reconstruction capabilities. Numerical examples support this conclusion.

Improved Sampling Methods for Shape Reconstruction of 3-D Buried Targets

This paper addresses the problem of reconstructing geometrical features of 3-D targets embedded into a nonaccessible region from multiview multistatic scattered field data. Sampling methods (SM) are simple and computationally effective approaches to pursue this task. However, their implementation requires a large number of multipolarization sources and probes. Moreover, their performances are often unsatisfactory for aspect-limited measurement configurations and lossy media. In order to tackle these drawbacks, usually faced in subsurface imaging, we propose a simplified and improved formulation based on the physical interpretation of SM. In particular, such a formulation relies on a small number of single polarization probes and exploits multifrequency data, for the first time in the framework of SM. The performances of the resulting approach are verified by monitoring 3-D regions of large extent.

On Quantitative Microwave Tomography of Female Breast

Microwave tomography deserves attention in biomedical imaging, owing to its potential capability of providing a morphological and functional assessment of the inspected tissues. However, such a goal requires the not trivial task of solving a non linear inverse scattering problem. In this paper, the factors afiecting the complexity of the inverse problem are exploited to trace guidelines aimed at setting the matching ∞uid, the frequency range and the number of probes in such a way that the dielectric parameters of female breast tissues can be reliably retrieved. Examples, concerning 2D realistic numerical phantoms obtained by NMR images, are given to asses a posteriori the efiectiveness of the proposed guidelines.

The Linear Sampling Method as a Way to Quantitative Inverse Scattering

The linear sampling method (LSM) is a simple and effective approach to image the shape of unknown targets via the solution of a linear inverse problem. In this paper, we show that the LSM can also be exploited to devise a novel effective approximation of the scattering phenomenon, that leads to a new noniterative linear inversion method for the estimation of the targets electric contrast. Since the introduced approximation relies on the broad applicability of the LSM, the proposed inversion method is suitable to tackle inverse scattering problems involving nonweak scatterers. As such, it represents an innovative, yet effective, way to tackle quantitative imaging. Examples with numerical and experimental data are given to show the performance of the approach. In particular, results obtained with Fresnel data-sets show that the proposed method is capable of successfully imaging targets which have been so far processed using nonlinear iterative schemes and taking advantage of frequency diversity.

Degree of nonlinearity and a new solution procedure in scalar two-dimensional inverse scattering problems.

Within the framework of inverse scattering problems, the quantifying of the degree of nonlinearity of the problem at hand provides an interesting possibility for evaluating the validity range of the Born series and for quantifying the difficulty of both forward and inverse problems. With reference to the two-dimensional scalar problem, new tools are proposed that allow the determination of the degree of nonlinearity in scattering problems when the maximum value, dimensions, and spatial-frequency content of the unknown permittivity are changed at the same time. As such, the proposed tools make it possible to identify useful guidelines for the solution of both forward and inverse problems and suggest an effective solution procedure for the latter. Numerical examples are reported to confirm the usefulness of the tools introduced and of the procedure proposed.

Inverse scattering from phaseless measurements of the total field on a closed curve

A new approach for quantitative electromagnetic imaging of scatterers located in free space from phaseless data is proposed and discussed. The procedure splits the problem into two steps. In the first one, we solve a phase-retrieval problem for the total field, thus estimating the amplitude and phase of the scattered field. Careful analysis of properties and possible representations of both scattered and incident fields allow us to introduce a criterion for an optimal choice of the measurement setup and a successful retrieval. Then the complex permittivity profile is reconstructed in the second step by use of the estimated scattered field. Numerical examples are provided to check the whole chain in the presence of noise-corrupted data.

BISTATIC TOMOGRAPHIC GPR IMAGING FOR INCIPIENT PIPELINE LEAKAGE EVALUATION

In this work, we present an inverse scattering approach to address the timely detection of damage and leakage from pipelines via multi-bistatic ground penetrating radar (GPR) surveys. The approach belongs to the class of linearized distorted wave models and explicitly accounts for the available knowledge on the investigated scenario in terms of pipe position and size. The inversion is regularized by studying the properties of the relevant linear operator in such a way to guarantee an early warning capability. The approach has been tested by means of synthetic data generated via a flnite-difierence time- domain forward solver capable of accurately and realistically modeling GPR experiments. The achieved results show that it is possible to detect the presence of leakage even in its flrst stages of development.

Improving the reconstruction capabilities in inverse scattering problems by exploitation of close-proximity setups

It has recently been shown that the measurement setups usually adopted in inverse scattering problems, in which the primary sources and the receiving antennas are placed at some wavelength apart from the object under test, suffer from intrinsic limitations in the reconstruction capabilities because of the essentially finite-dimensional nature of the space of data (the scattered fields). To investigate whether it is possible to overcome these limitations, two (novel to our knowledge) measurement configurations for inverse scattering experiments at a fixed frequency are analyzed and discussed. By means of an analysis of the properties of the radiation operator, it is shown that positioning the measurement probes (and possibly the primary sources) in the close proximity of the object under test allows an improvement of the reconstruction capabilities of inversion algorithms with respect to conventional setups. However, such an improvement can be achieved only in a region close to the border of the region under test. Quantitative rules for the achievable improvement are given and are exemplified through numerical examples.

Optimal Constrained Field Focusing for Hyperthermia Cancer Therapy: a Feasibility Assessment on Realistic Phantoms

Microwave hyperthermia is a non-invasive treatment for cancer which exploits a selective heating of tissues induced through focused electromagnetic flelds. In order to improve the treatments e-ciency, while minimizing side efiects, it is necessary to achieve a constrained focusing of the fleld radiated by the sources. To address this issue, in this paper we present an innovative and computationally efiective approach to the fleld focusing for hyperthermia. The proposed method, after establishing the number of sources to be used, determines the excitations of the given set of sources such to produce a maximum fleld in a given region of space, subject to a completely arbitrary mask for the fleld amplitude in all other regions. As the approach relies on a formulation of the problem in terms of convex programming, it is able to achieve the globally optimal solution without the adoption of computationally intensive global optimization procedures. A preliminary assessment of feasibility is given on hyperthermia therapy of breast cancer by means of numerical examples run on realistic 2D phantoms of female breast.