Unrolled Optimization via Physics-Assisted Convolutional Neural Network for MR-Based Electrical Properties Tomography: A Numerical Investigation.

Magnetic Resonance imaging based Electrical Properties Tomography (MR-EPT) is a non-invasive technique that measures the electrical properties (EPs) of biological tissues. In this work, we present and numerically investigate the performance of an unrolled, physics-assisted method for 2D MR-EPT reconstructions, where a cascade of Convolutional Neural Networks is used to compute the contrast update. Each network takes in input the EPs and the gradient descent direction (encoding the physics underlying the adopted scattering model) and returns as output the updated contrast function. The network is trained and tested in silico using 2D slices of realistic brain models at 128 MHz. Results show the capability of the proposed procedure to reconstruct EPs maps with quality comparable to that of the popular Contrast Source Inversion-EPT, while significantly reducing the computational time.

In-Vivo Electrical Properties Estimation of Biological Tissues by Means of a Multi-Step Microwave Tomography Approach.

The accurate quantitative estimation of the electromagnetic properties of tissues can serve important diagnostic and therapeutic medical purposes. Quantitative microwave tomography is an imaging modality that can provide maps of the in-vivo electromagnetic properties of the imaged tissues, i.e. both the permittivity and the electric conductivity. A multi-step microwave tomography approach is proposed for the accurate retrieval of such spatial maps of biological tissues. The underlying idea behind the new imaging approach is to progressively add details to the maps in a step-wise fashion starting from single-frequency qualitative reconstructions. Multi-frequency microwave data is utilized strategically in the final stage. The approach results in improved accuracy of the reconstructions compared to inversion of the data in a single step. As a case study, the proposed workflow was tested on an experimental microwave data set collected for the imaging of the human forearm. The human forearm is a good test case as it contains several soft tissues as well as bone, exhibiting a wide range of values for the electrical properties.

Field and Temperature Shaping for Microwave Hyperthermia: Recent Treatment Planning Tools to Enhance SAR-Based Procedures.

The aim of the article is to provide a summary of the work carried out in the framework of a research project funded by the Italian Ministry of Research. The main goal of the activity was to introduce multiple tools for reliable, affordable, and high-performance microwave hyperthermia for cancer therapy. The proposed methodologies and approaches target microwave diagnostics, accurate in vivo electromagnetic parameters estimation, and improvement in treatment planning using a single device. This article provides an overview of the proposed and tested techniques and shows their complementarity and interconnection. To highlight the approach, we also present a novel combination of specific absorption rate optimization via convex programming with a temperature-based refinement method implemented to mitigate the effect of thermal boundary conditions on the final temperature map. To this purpose, numerical tests were carried out for both simple and anatomically detailed 3D scenarios for the head and neck region. These preliminary results show the potential of the combined technique and improvements in the temperature coverage of the tumor target with respect to the case wherein no refinement is adopted.

An Affordable Streamflow Measurement Technique Based on Delay and Sum Beamforming.

At the local scale, environmental parameters often require monitoring by means of affordable measuring techniques and technologies given they need to be frequently surveyed. Streamflow in riverbeds or in channels is a hydrological variable that needs to be monitored in order to keep the runoff regimes under control and somehow forecast floods, allowing prevention of damage for people and infrastructure. Moreover, measuring such a variable is always extremely important for the knowledge of the environmental status of connected aquatic ecosystems. This paper presents a new approach to assessing hydrodynamic features related to a given channel by means of a beamforming technique that was applied to video sensing. Different features have been estimated, namely the flow velocity, the temperature, and the riverbed movements. The applied beamforming technique works on a modified sum and delay method, also using the Multiple Signal Classification algorithm (MUSIC), by acting as Synthetic Aperture Radar (SAR) post-processing. The results are very interesting, especially compared to the on-site measured data and encourage the use of affordable video sensors located along the channel or river course for monitoring purposes. The paper also illustrates the use of beamforming measurements to be calibrated by means of conventional techniques with more accurate data. Certainly, the results can be improved; however, they indicate some margins of improvements and updates. As metrics of assessment, a histogram of greyscale/pixels was adopted, taking into account the example of layers and curve plots. They show changes according to the locations where the supporting videos were obtained.

Predictive value of SAR based quality indicators for head and neck hyperthermia treatment quality.

PURPOSE: Hyperthermia treatment quality determines treatment effectiveness as shown by the clinically derived thermal-dose effect relations. SAR based optimization factors are used as possible surrogate for temperature, since they are not affected by thermal tissue properties uncertainty and variations. Previously, target coverage (TC) at the 25% and 50% iso-SAR level was shown predictive for treatment outcome in superficial hyperthermia and the target-to-hot-spot-quotient (THQ) was shown to highly correlate with predictive temperature in deep pelvic hyperthermia. Here, we investigate the correlation with temperature for THQ and TC using an 'intermediate' scenario: semi-deep hyperthermia in the head & neck region using the HYPERcollar3D. METHODS: Fifteen patient-specific models and two different planning approaches were used, including random perturbations to circumvent optimization bias. The predicted SAR indicators were compared to predicted target temperature distribution indicators T50 and T90, i.e., the median and 90th percentile temperature respectively. RESULTS: The intra-patient analysis identified THQ, TC25 and TC50 as good temperature surrogates: with a mean correlation coefficient R2T50 = 0.72 and R2T90=0.66. The inter-patient analysis identified the highest correlation with TC25 (R2T50 = 0.76, R2T90=0.54) and TC50 (R2T50 = 0.74, R2T90 = 0.56). CONCLUSION: Our investigation confirmed the validity of our current strategy for deep hyperthermia in the head & neck based on a combination of THQ and TC25. TC50 was identified as the best surrogate since it enables optimization and patient inclusion decision making using one single parameter.

Towards Printable Natural Dielectric Cloaks via Inverse Scattering Techniques.

The synthesis of non-magnetic 2D dielectric cloaks as proper solutions of an inverse scattering problem is addressed in this paper. Adopting the relevant integral formulation governing the scattering phenomena, analytic and numerical approaches are exploited to provide new insights on how frequency and direction of arrival of the incoming wave may influence the cloaking mechanism in terms of permittivity distribution within the cover region. In quasi-static (subwavelength) regime a solution is analytically derived in terms of homogeneous artificial dielectric cover with ε < ε 0, which is found to be a necessary and sufficient condition for achieving omnidirectional cloaking. On the other hand, beyond quasi-static regime, the cloaking problem is addressed as an optimization task looking for only natural dielectric coatings with ε > ε 0 able to hide the object for a given number of directions of the incident field. Simulated results confirm the validity of both analytic and numerical methodologies and allow to estimate effective bandwidths both in terms of frequency range and direction of arrival of the impinging field.

Microwave frequency sweep interferometer for plasma density measurements in ECR ion sources: Design and preliminary results.

The Electron Cyclotron Resonance Ion Sources (ECRISs) development is strictly related to the availability of new diagnostic tools, as the existing ones are not adequate to such compact machines and to their plasma characteristics. Microwave interferometry is a non-invasive method for plasma diagnostics and represents the best candidate for plasma density measurement in hostile environment. Interferometry in ECRISs is a challenging task mainly due to their compact size. The typical density of ECR plasmas is in the range 10(11)-10(13) cm(-3) and it needs a probing beam wavelength of the order of few centimetres, comparable to the chamber radius. The paper describes the design of a microwave interferometer developed at the LNS-INFN laboratories based on the so-called "frequency sweep" method to filter out the multipath contribution in the detected signals. The measurement technique and the preliminary results (calibration) obtained during the experimental tests will be presented.

Phaseless imaging with experimental data: facts and challenges.

Two-dimensional target characterization using inverse profiling approaches with total-field phaseless data is discussed. Two different inversion schemes are compared. In the first one, the intensity-only data are exploited in a minimization scheme, thanks to a proper definition of the cost functional. Specific normalization and starting guess are introduced to avoid the need for global optimization methods. In the second scheme [J. Opt. Soc. Am. A21, 622 (2004)], one exploits the field properties and the theoretical results on the inversion of quadratic operators to derive a two-step solution strategy, wherein the (complex) scattered fields embedded in the available data are retrieved first and then a traditional inverse scattering problem is solved. In both cases, the analytical properties of the fields allow one to properly fix the measurement setup and identify the more convenient strategy to adopt. Also, indications on the number and types of sources and receivers to be used are given. Results from experimental data show the efficiency of these approaches and the tools introduced.

Generalized scattering-matrix method for the analysis of two-dimensional photonic bandgap devices.

Development of accurate numerical methods for the analysis of photonic-bandgap-based devices is a relevant issue in optimizing existing devices and/or developing new design solutions. Within this framework, we present an innovative and general approach for the evaluation of the electromagnetic behavior of two-dimensional finite-extent photonic crystals made of a finite set of parallel rods. The proposed approach is a generalization of the scattering-matrix method introduced by Maystre and co-workers and of its improved version proposed by the present authors, which exploits a suitable aggregation into "macrocells" to achieve a reduction of the number of unknowns. As a matter of fact, both of these approaches can be exploited only in those cases in which particular modal expansions for the fields hold true. In order to overcome this limitation, we propose a suitable exploitation of the method of auxiliary sources to provide a general and reliable method for the numerical computation of the scattering matrix of an object of arbitrary shape. By taking advantage of this, we can then generalize our improved scattering matrix method to further increase its computational effectiveness. A numerical analysis of some square-lattice configurations is reported to confirm the accuracy of the proposed method and the remarkable computational benefit.

Faithful non-linear imaging from only-amplitude measurements of incident and total fields.

Applicability of inverse scattering based imaging procedures can be broadened by developing new approaches exploiting only amplitude data. As a matter of fact, this can open the way to simpler and less expensive measurement set-ups. In this respect, a two-step based procedure for solving electromagnetic nonlinear inverse scattering problems from only amplitude measurements of the total field has been recently proposed [1,2]. However, in these latter both amplitude and phase of the incident field are still required. In this contribution, we show the possibility of achieving this information from the measured amplitude distribution of the incident field on the observation domain. In particular, a three steps imaging technique which exploits only amplitude measurements of the total and incident fields has been developed. The proposed procedure has been tested against benchmark experimental data available in the literature. The obtained results fully confirm the possibility of achieving faithful reconstructions of unknown targets without performing any phase measurements and any approximation on the scattering equations involved in the inverse scattering problems.

Inverse scattering from phaseless measurements of the total field on open lines.

A new solution approach to inverse scattering from aspect-limited phaseless measurements of the total field is introduced and discussed. In analogy with the case of measurements on closed curves [J. Opt. Soc. Am. A21, 622 (2004)], the procedure splits the problem into two different steps. In the first step, amplitude and phase of the scattered field are estimated from only amplitude information of the total field. By properly extending the concept of reduced radiated field to the case of scattered fields (as a function of both illumination and measurement variables) and taking advantage of the properties of the square amplitude distribution of the total field, criteria are given for an optimal choice of the measurement setup and a successful retrieval. Then the complex permittivity profile is reconstructed in the second step, starting from the scattered fields estimated in the previous step. Numerical examples are provided to assess the effectiveness of the whole chain in the presence of noise-corrupted data and the relevance of the representation introduced for the scattered fields.

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.