Multifractal analysis with the probability density function at the three-dimensional Anderson transition

The probability density function (PDF) for critical wavefunction amplitudes is studied in the three-dimensional Anderson model. We present a formal expression between the PDF and the multifractal spectrum f(alpha) in which the role of finite-size corrections is properly analyzed. We show the non-gaussian nature and the existence of a symmetry relation in the PDF. From the PDF, we extract information about f(alpha) at criticality such as the presence of negative fractal dimensions and we comment on the possible existence of termination points. A PDF-based multifractal analysis is hence shown to be a valid alternative to the standard approach based on the scaling of general inverse participation ratios.Comment: 4 pages, 7 figure

Multi-shot Calibration Technique for Microwave Imaging Systems

This paper proposes a novel “multi-shot” calibration technique that reduces imaging microwave reconstructions artifacts, compensating for uncontrolled variations during the measuring process and later propagated in the inversion. The calibration combines different consecutive sets of measured data with simulated ones in a post-processing stage, providing benefits without the need for additional experimental reference calibrations. The proposed scheme is tested experimentally in a non-trivial scenario. A microwave scanner images an early-stage hemorrhagic stroke in the left parietal lobe, applying a differential imaging algorithm based on the truncated singular value decomposition. Though, the proposed mechanisms can be used for other microwave imaging devices. The results reveal that the calibration procedure improves the quality of the retrieved images compared to the non-calibrated approach, cleaning the images and making the interpretation of imaged contrast variation easier

Partitioning Schemes and Non-Integer Box Sizes for the Box-Counting Algorithm in Multifractal Analysis

We compare different partitioning schemes for the box-counting algorithm in the multifractal analysis by computing the singularity spectrum and the distribution of the box probabilities. As model system we use the Anderson model of localization in two and three dimensions. We show that a partitioning scheme which includes unrestricted values of the box size and an average over all box origins leads to smaller error bounds than the standard method using only integer ratios of the linear system size and the box size which was found by Rodriguez et al. (Eur. Phys. J. B 67, 77-82 (2009)) to yield the most reliable results.Comment: 10 pages, 13 figure

Hybrid Simulation-Measurement Calibration Technique for Microwave Imaging Systems

This paper proposes an innovative technique to calibrate microwave imaging (MWI) systems combining available measured data with simulated synthetic ones. The introduced technique aims to compensate the variations of the antenna array due to unavoidable manufacturing tolerances and placement, in comparison to the nominal electromagnetic (EM) scenario. The scheme is tested virtually and experimentally for the MWI of the adult human head tissues. The virtual EM analysis uses a realistic 3-D CAD model working together with a full-wave software, based on the finite element method. Meanwhile, the real implementation employs a single-cavity anthropomorphic head phantom and a custom brick-shaped antenna array working at around 1 GHz

Moving Forward to Real-time Imaging-based Monitoring of Cerebrovascular Diseases Using a Microwave Device: Numerical and Experimental Validation

This paper introduces a numerical and experimental assessment of the microwave device capabilities to perform continuous real-time imaging-based monitoring of a brain stroke, exploiting a differential measuring scheme of the scattering matrices and the distorted Born approximation. The device works around 1 GHz and consists of a low-complexity 22-antenna-array composed of custom-made wearable elements. The imaging kernel is built using an average-head reference scenario computed off-line via accurate numerical models and an in-house finite element method electromagnetic solver. The validation follows the progression of emulated evolving hemorrhagic stroke condition, including tests with both an average single-tissue head model and a multi-tissue one in the numerical part and the average scenario in the experimental one. The results show the system's capacity to localize and track the shape changes of the stroke-affected area in all studied cases

Hybrid imaging kernel calibration applied on microwave scanner for brain stroke monitoring

This paper validates a calibration procedure applied on a microwave imaging (MWI) kernel based on the combination of pre-computed simulated data and available S-parameters measurements. The assessed technique compensates for the image degradation caused by mild and non-modeled features of the imaging device, such as the unavoidable manufacturing discrepancies in the antenna array. The testing considers a synthetically mimicked experimental scenario of a hemorrhagic stroke condition and a realistic scanner prototype. This approach allows a thorough comparative assessment of the calibration effect on the electric field estimation used by the MWI algorithm, hardly achievable with measurements. The results show the capability of the calibration procedure to reduce the retrieved images’ distortions and artifacts compared to the non-calibrated approach, being an essential milestone toward its application in real-life scenarios

Brick Shaped Antenna Module for Microwave Brain Imaging Systems

In this letter, we describe and validate a microwave antenna designed for an imaging device for the diagnosis and monitoring of cerebrovascular pathologies. The antenna consists of a printed monopole immersed in a parallelepipedic block of semiflexible material with custom-permittivity, which allows to avoid the use of liquid coupling media and enables a simple array arrangement. The “brick” is built with a mixture of urethane rubber and graphite powder. The -10 dB frequency band of the antenna is 800 MHz-1.2 GHz, in agreement with the device requirements. The designed brick antenna is assessed in terms of power penetration, reflection, and transmission coefficients. To show the performance of the antenna in the relevant application scenario, an experiment has been carried out on an anthropomorphic head phantom, measuring the differential signals between healthy state and hemorrhagic stroke mimicking condition for different antennas positions

Assessing a Microwave Imaging System for Brain Stroke Monitoring via High Fidelity Numerical Modelling

This work presents the outcomes of a numerical analysis based on a 3-D high fidelity model of a realistic microwave imaging system for the clinical follow-up of brain stroke. The analysis is meant as a preliminary step towards the full experimental characterization of the system, with the aim of assessing the achievable results and highlight possible critical points. The system consists of an array of twenty-four printed monopole antennas, placed conformal to the upper part of the head; each monopole is immersed into a semi-solid dielectric brick with custom permittivity, acting as coupling medium. The whole system, including the antennas and their feeding mechanism, has been numerically modeled via a custom full-wave software based on the finite element method. The numerical model generates reliable electromagnetic operators and accurate antenna scattering parameters, which provide the input data for the implemented imaging algorithm. In particular, the numerical analysis assesses the capability of the device of reliably monitoring the evolution of hemorrhages and ischemias, considering the progression from a healthy statet o an early-stage stroke