Subcranial Encephalic Temnograph-Shaped Helmet for Brain Stroke Monitoring.

In this contribution, a wearable microwave imaging system for real-time monitoring of brain stroke in the post-acute stage is described and validated. The system exploits multistatic/multifrequency (only 50 frequency samples) data collected via a low-cost and low-complexity architecture. Data are collected by an array of only 16 antennas moved by pneumatic system. Phantoms, built from ABS material and filled with appropriate Triton X-100-based mixtures to mimic the different head human tissues, are employed for the experiments. The microwave system exploits the differential scattering measures and the Incoherent MUSIC algorithm to provide a 3D image of the region under investigation. The shown results, although preliminary, confirm the potential of the proposed microwave system in providing reliable results, including for targets whose evolution is as small as 16 mL in volume.

Spectral Methods for Response Enhancement of Microwave Resonant Sensors in Continuous Non-Invasive Blood Glucose Monitoring.

In this paper, the performance of three recent algorithms for the frequency-response enhancement of microwave resonant sensors are compared. The first one, a single-step algorithm, is based on a couple of direct-inverse Fourier transforms, giving a densely sampled response as a result. The second algorithm exploits an iterative procedure to progressively restricts the frequency response. The final one is based on the super-resolution MUSIC algorithm. The comparison is carried out through a Monte Carlo analysis. In particular, synthetic signals are firstly exploited to mimic the frequency response of a resonant microwave sensor. Then, experimental data collected from water-glucose solutions are adopted as validation test for potential applications in noninvasive blood-glucose monitoring.

Experimental Validation of a Microwave Imaging Method for Shallow Buried Target Detection by Under-Sampled Data and a Non-Cooperative Source.

In microwave imaging, it is often of interest to inspect electrically large spatial regions. In these cases, data must be collected over a great deal of measurement points which entails long measurement time and/or costly, and often unfeasible, measurement configurations. In order to counteract such drawbacks, we have recently introduced a microwave imaging algorithm that looks for the scattering targets in terms of equivalent surface currents supported over a given reference plane. While this method is suited to detect shallowly buried targets, it allows one to independently process all frequency data, and hence the source and the receivers do not need to be synchronized. Moreover, spatial data can be reduced to a large extent, without any aliasing artifacts, by properly combining single-frequency reconstructions. In this paper, we validate such an approach by experimental measurements. In particular, the experimental test site consists of a sand box in open air where metallic plate targets are shallowly buried a (few cm) under the air/soil interface. The investigated region is illuminated by a fixed transmitting horn antenna, whereas the scattered field is collected over a planar measurement aperture at a fixed height from the air-sand interface. The transmitter and the receiver share only the working frequency information. Experimental results confirm the feasibility of the method.

Incoherent Radar Imaging for Breast Cancer Detection and Experimental Validation against 3D Multimodal Breast Phantoms.

In this paper we consider radar approaches for breast cancer detection. The aim is to give a brief review of the main features of incoherent methods, based on beam-forming and Multiple SIgnal Classification (MUSIC) algorithms, that we have recently developed, and to compare them with classical coherent beam-forming. Those methods have the remarkable advantage of not requiring antenna characterization/compensation, which can be problematic in view of the close (to the breast) proximity set-up usually employed in breast imaging. Moreover, we proceed to an experimental validation of one of the incoherent methods, i.e., the I-MUSIC, using the multimodal breast phantom we have previously developed. While in a previous paper we focused on the phantom manufacture and characterization, here we are mainly concerned with providing the detail of the reconstruction algorithm, in particular for a new multi-step clutter rejection method that was employed and only barely described. In this regard, this contribution can be considered as a completion of our previous study. The experiments against the phantom show promising results and highlight the crucial role played by the clutter rejection procedure.

Scattered Far-Field Sampling in Multi-Static Multi-Frequency Configuration.

This paper deals with an inverse scattering problem under a linearized scattering model for a multi-static/multi-frequency configuration. The focus is on the determination of a sampling strategy that allows the reduction of the number of measurement points and frequencies and at the same time keeping the same achievable performance in the reconstructions as for full data acquisition. For the sake of simplicity, a 2D scalar geometry is addressed, and the scattered far-field data are collected. The relevant scattering operator exhibits a singular value spectrum that abruptly decays (i.e., a step-like behavior) beyond a certain index, which identifies the so-called number of degrees of freedom (NDF) of the problem. Accordingly, the sampling strategy is derived by looking for a discrete finite set of data points for which the arising semi-discrete scattering operator approximation can reproduce the most significant part of the singular spectrum, i.e., the singular values preceding the abrupt decay. To this end, the observation variables are suitably transformed so that Fourier-based arguments can be used. The arising sampling grid returns several data that is close to the NDF. Unfortunately, the resulting data points (in the angle-frequency domain) leading to a complicated measurement configuration which requires collecting the data at different spatial positions for each different frequency. To simplify the measurement configuration, a suboptimal sampling strategy is then proposed which, by an iterative procedure, enforces the sampling points to belong to a rectangular grid in the angle-frequency domain. As a result of this procedure, the overall data points (i.e., the couples angle-frequency) actually increase but the number of different angles and frequencies reduce and lead to a measurement configuration that is more practical to implement. A few numerical examples are included to check the proposed sampling scheme.

Multimodal Breast Phantoms for Microwave, Ultrasound, Mammography, Magnetic Resonance and Computed Tomography Imaging.

The aim of this work was to develop multimodal anthropomorphic breast phantoms suitable for evaluating the imaging performance of a recently-introduced Microwave Imaging (MWI) technique in comparison to the established diagnostic imaging modalities of Magnetic Resonance Imaging (MRI), Ultrasound (US), mammography and Computed Tomography (CT). MWI is an emerging technique with significant potential to supplement established imaging techniques to improve diagnostic confidence for breast cancer detection. To date, numerical simulations have been used to assess the different MWI scanning and image reconstruction algorithms in current use, while only a few clinical trials have been conducted. To bridge the gap between the numerical simulation environment and a more realistic diagnostic scenario, anthropomorphic phantoms which mimic breast tissues in terms of their heterogeneity, anatomy, morphology, and mechanical and dielectric characteristics, may be used. Key in this regard is achieving realism in the imaging appearance of the different healthy and pathologic tissue types for each of the modalities, taking into consideration the differing imaging and contrast mechanisms for each modality. Suitable phantoms can thus be used by radiologists to correlate image findings between the emerging MWI technique and the more familiar images generated by the conventional modalities. Two phantoms were developed in this study, representing difficult-to-image and easy-to-image patients: the former contained a complex boundary between the mammary fat and fibroglandular tissues, extracted from real patient MRI datasets, while the latter contained a simpler and less morphologically accurate interface. Both phantoms were otherwise identical, with tissue-mimicking materials (TMMs) developed to mimic skin, subcutaneous fat, fibroglandular tissue, tumor and pectoral muscle. The phantoms' construction used non-toxic materials, and they were inexpensive and relatively easy to manufacture. Both phantoms were scanned using conventional modalities (MRI, US, mammography and CT) and a recently introduced MWI radar detection procedure called in-coherent Multiple Signal Classification (I-MUSIC). Clinically realistic artifact-free images of the anthropomorphic breast phantoms were obtained using the conventional imaging techniques as well as the emerging technique of MWI.

Depth resolution in strip current reconstructions in near non-reactive zone.

The problem of reconstructing a strip electric current from its radiated field collected over a bounded finite rectilinear observation domain, orthogonal and centered with respect to the source, is dealt with. In particular, the study is developed for a two-dimensional, scalar geometry and focuses on the estimation of achievable performance in terms of the number of degrees of freedom (NDF) and depth resolution. This is a classical problem that we contributed to in the past by addressing a Fresnel zone configuration. Here, the plan is to expand those results by removing the geometrical limitations due to the Fresnel approximation. The main idea is to rewrite the involved radiation operator as a Fourier-type integral operator by introducing a suitable variable transformation. This allows applying simple Fourier-based reasoning to estimate the achievable point-spread function, which in turn is used to estimate the NDF and depth resolution. The obtained NDF and depth resolution estimations are compared to those returned by numerical computation of the relevant singular value decomposition, and very good agreement is found. Moreover, it is shown that the results obtained for the Fresnel zone are a particularization of the new findings when such an approximation holds true.

Resolution limits in inverse source problem for strip currents not in Fresnel zone.

This paper deals with the classical question of estimating achievable resolution in terms of configuration parameters in inverse source problems. In particular, the study is developed for two-dimensional prototype geometry, where a strip source (magnetic or electric) is to be reconstructed from its radiated field observed over a bounded rectilinear domain parallel to the source. Resolution formulas are well known when the field is collected in the far field or in the Fresnel zone of the source. Here, the plan is to expand those results by removing the geometrical limitations due to the far field or Fresnel approximations. To this end, the involved radiation operators are recast as Fourier-type integral operators upon introducing suitable variable transformations. For magnetic sources, this allows one to find a closed-form approximation of the singular system and hence to estimate achievable resolution, the latter given as the main beam width of the point-spread function. Unfortunately, this does not happen for electric currents. In this case, the radiation operator is inverted by a weighted adjoint inversion method (a back-propagation-like method) that directly allows one to find an analytical expression of the point-spread function and hence of the resolution. The derived resolution formulas are the same for magnetic and electric currents; they clearly point out the role of geometrical parameters and coincide with the one pertaining to the Fresnel zone when the geometry verifies the Fresnel approximation. A few numerical examples are also enclosed to check the theory.

Sampling approach for singular system computation of a radiation operator.

The problem of computing the singular system of the radiation operator pertaining to the case of strip currents is dealt with. The associate eigenvalue problem involves a space-variant operator whose kernel is not band-limited. As a consequence, the sampling approach, which has been recently introduced for computing the eigenwavefronts of some band-limited linear space-invariant imaging systems, cannot be used as such. To overcome this drawback, it is shown that the kernel function can be recast as a varying band-limited function. This allows exploiting the pseudo-sampling series theory from which a sampling approximation of the kernel function is derived and eventually used to set the discrete eigenvalue problem. In particular, unlike the classical sampling approach, the sampling points turn out to be non-uniformly distributed. Some numerical examples are used to check the theory. It is shown that the most significant part of the singular system can be very accurately computed by using a number of samples slightly greater than the Shannon number.

Image-Based RCS Estimation from Near-Field Data.

This paper deals with the problem of estimating the RCS from near-field data by image-based approaches. In particular, a rigorous focusing procedure based on a weighted adjoint scheme, which is also applicable to an arbitrary measurement curve, is developed. The developed formalism allows us to address the important question concerning the need to employ a multi-frequency configuration to estimate the RCS. Accordingly, it is shown that if RCS is required at a given frequency, then the target image obtained solely at such a frequency can be exploited provided that the spatial truncation arising from the size of the investigated area is properly taken into account.

Inverse source in the near field: the case of a strip current.

In this paper, we consider an inverse source problem in the near zone for a prototype configuration where the field radiated by a bounded strip magnetic current is observed over a rectilinear and parallel (to the source) observation domain. The study focuses on how the achievable performance depends on the configuration's geometric parameters and the noise. In particular, we succeed in working out an approximation for the singular spectrum of the pertinent radiation operator that allows us to obtain analytical estimations for the resolution, the number of degrees of freedom, and the information content. Remarkably, the role of evanescent waves, which become relevant in the very near zone, is highlighted in connection to the available signal-to-noise ratio.

Data-driven linearizing approach in inverse scattering.

Direct or forward wave scattering admits three classical regimes in which the map from scatterer properties or scattering potential to the data is linear, namely, the Born, Rytov, and physical optics approximations. In this paper we derive a new decomposition of the forward scattering map which reveals a previously unknown approximate bilinear forward scattering relation. The latter is data-driven, i.e., it involves exact scattering data, and has the useful property that the dependence on the data and the potential is bilinear. This fundamental result naturally leads to a new linear inverse scattering approach that generalizes and is more broadly applicable than the classical Born-approximation-based imaging. The developed scattering and inverse scattering theory are presented in both plane wave and multipole expansion representations, and the possibility of exploiting support information is also formally addressed in the multipole domain. The paper includes computer simulations illustrating the derived theory and algorithms.

A COTS-Based Microwave Imaging System for Breast-Cancer Detection.

Microwave imaging is an emerging breast cancer diagnostic technique, which aims at complementing already established methods like mammography, magnetic resonance imaging, and ultrasound. It offers two striking advantages: no-risk for the patient and potential low-cost for national health systems. So far, however, the prototypes developed for validation in labs and clinics used costly lab instruments such as a vector network analyzer (VNA). Moreover, the CPU time required by complex image reconstruction algorithms may not be compatible with the duration of a medical examination. In this paper, both these issues are tackled. Indeed, we present a prototype system based on low-cost and off-the-shelf microwave components, custom-made antennas, and a small form-factor processing system with an embedded field-programmable gate array for accelerating the execution of the imaging algorithm. We show that our low-cost system can compete with an expensive VNA in terms of accuracy, and it is more than 20x faster than a high-performance server at image reconstruction.

Microwave bone imaging: a preliminary scanning system for proof-of-concept.

This Letter introduces a feasibility study of a scanning system for applications in biomedical bone imaging operating in the microwave range 0.5-4 GHz. Mechanical uncertainties and data acquisition time are minimised by using a fully automated scanner that controls two antipodal Vivaldi antennas. Accurate antenna positioning and synchronisation with data acquisition enables a rigorous proof-of-concept for the microwave imaging procedure of a multi-layer phantom including skin, fat, muscle and bone tissues. The presence of a suitable coupling medium enables antenna miniaturisation and mitigates the impedance mismatch between antennas and phantom. The three-dimensional image of tibia and fibula is successfully reconstructed by scanning the multi-layer phantom due to the distinctive dielectric contrast between target and surrounding tissues. These results show the viability of a microwave bone imaging technology which is low cost, portable, non-ionising, and does not require specially trained personnel. In fact, as no a-priori characterisation of the antenna is required, the image formation procedure is very conveniently simplified.

Beamforming and holography image formation methods: an analytic study.

Beamforming and holographic imaging procedures are widely used in many applications such as radar sensing, sonar, and in the area of microwave medical imaging. Nevertheless, an analytical comparison of the methods has not been done. In this paper, the Point Spread Functions pertaining to the two methods are analytically determined. This allows a formal comparison of the two techniques, and to easily highlight how the performance depends on the configuration parameters, including frequency range, number of scatterers, and data discretization. It is demonstrated that the beamforming and holography basically achieve the same resolution but beamforming requires a cheaper (less sensors) configuration..

Fault detection in dielectric grid scatterers.

The problem of diagnosing a grid of small (in terms of the probing wavelength) dielectric scatterers is considered. The aim is to detect and locate possible defects occurring within a known grid when one (or more) scatterer is removed/missing (fault). The study is developed for the canonical case of a TM scalar two-dimensional geometry with the scatterers consisting of dielectric cylinders of small circular cross section. The scattering by a fault is modeled by relaying only to a priori information about the complete grid which leads to a numerically effective inversion procedures as the bulk of the numerical effort is to be done only once. Inversion is achieved by a truncated singular value decomposition scheme and results are provided in terms of closed form expressions for the probability of detection and of false alarm. This allows us to foreseen the achievable performance and to highlight the role of scattering configuration parameters. Numerical examples are also enclosed to corroborate theoretical outcomes. The case of two or more faults is considered as well. For such a case it is numerically shown that detection method still works well even though multiple scattering (occurring between faults) is neglected.

Breast cancer detection using interferometric MUSIC: experimental and numerical assessment.

PURPOSE: In microwave breast cancer detection, it is often beneficial to arrange sensors in close proximity to the breast. The resultant coupling generally changes the antenna response. As an a priori characterization of the radio frequency system becomes difficult, this can lead to severe degradation of the detection efficacy. The purpose of this paper is to demonstrate the advantages of adopting an interferometric multiple signal classification (I-MUSIC) approach due to its limited dependence from a priori information on the antenna. The performance of I-MUSIC detection was measured in terms of signal-to-clutter ratio (SCR), signal-to-mean ratio (SMR), and spatial displacement (SD) and compared to other common linear noncoherent imaging methods, such as migration and the standard wideband MUSIC (WB-MUSIC) which also works when the antenna is not accounted for. METHODS: The data were acquired by scanning a synthetic oil-in-gelatin phantom that mimics the dielectric properties of breast tissues across the spectrum 1-3 GHz using a proprietary breast microwave multi-monostatic radar system. The phantom is a multilayer structure that includes skin, adipose, fibroconnective, fibroglandular, and tumor tissue with an adipose component accounting for 60% of the whole structure. The detected tumor has a diameter of 5 mm and is inserted inside a fibroglandular region with a permittivity contrast εr-tumor/εr-fibroglandular < 1.5 over the operating band. Three datasets were recorded corresponding to three antennas with different coupling mechanisms. This was done to assess the independence of the I-MUSIC method from antenna characterizations. The datasets were processed by using I-MUSIC, noncoherent migration, and wideband MUSIC under equivalent conditions (i.e., operative bandwidth, frequency samples, and scanning positions). SCR, SMR, and SD figures were measured from all reconstructed images. In order to benchmark experimental results, numerical simulations of equivalent scenarios were carried out by using CST Microwave Studio. The three numerical datasets were then processed following the same procedure that was designed for the experimental case. RESULTS: Detection results are presented for both experimental and numerical phantoms, and higher performance of the I-MUSIC method in comparison with the WB-MUSIC and noncoherent migration is achieved. This finding is confirmed for the three different antennas in this study. Although a delocalization effect occurs, experimental datasets show that the signal-to-clutter ratio and the signal-to-mean performance with the I-MUSIC are at least 5 and 2.3 times better than the other methods, respectively. The numerical datasets calculated on an equivalent phantom for cross-testing confirm the improved performance of the I-MUSIC in terms of SCR and SMR. In numerical simulations, the delocalization effect is dramatically reduced up to an SD value of 1.61 achieved with the I-MUSIC in combination with the antipodal Vivaldi antenna. This shows that mechanical uncertainties are the main reason for the delocalization effect in the measurements. CONCLUSIONS: Experimental results show that the I-MUSIC generates images with signal-to-clutter levels higher than 5.46 dB across all working conditions and it reaches 7.84 dB in combination with the antipodal Vivaldi antenna. Numerical simulations confirm this trend and due to ideal mechanical conditions return a signal-to-clutter level higher than 7.61 dB. The I-MUSIC largely outperforms the methods under comparison and is able to detect a 5-mm tumor with a permittivity contrast of 1.5.

Inverse source in the presence of a reflecting plane for the strip case.

In this paper the inverse source problem in the presence of a reflecting plane is dealt with for a two-dimensional configuration and bounded rectilinear strip sources. The cases of both orthogonal and parallel (to the reflecting plane) sources are considered. Analytical arguments are developed to estimate the singular value decomposition of the pertinent radiation operator. This allows highlighting of the role played by the reflecting plane in the so-called number of degrees of freedom of the radiated field as well as in the achievable resolution while reconstructing the unknown sources.

Role of diversity on the singular values of linear scattering operators: the case of strip objects.

The singular value decomposition of the far-zone scattering operator for weak strip-like scattering objects is studied under multiple view and/or multiple frequency illuminations. The aim is to highlight how such diversities impact the number of degrees of freedom (NDF) of the scattering problem. When the angles of incidence and/or frequencies vary within discrete finite sets, the singular values are analytically determined. It is shown that they exhibit a multistep behavior. For the continuous case, upper and lower bounds are found, which allows us to obtain estimations for the NDF dependending on the parameters of the configuration.

Fault detection in metallic grid scattering.

The canonical problem of detecting and localizing missing scatterers (faults) inside a known grid of small cross section perfect electric conducting cylinders is dealt with. The case of a TM scalar two-dimensional geometry is considered. The scattering by a fault is modeled as the radiation of a proper magnetic current, by exploiting the Green's function of the complete grid. An approximated linear model of the scattering is proposed and discussed in terms of the achievable probability of detection, also in the case of two faults, and checked against model error and noisy synthetic data.