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.

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.

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.

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.