Frequency-Domain Integral Equations of Scattering for Complex Scalar Responses

Beaverstone, Alexander S.; Shumakov, Denys S.; Nikolova, Natalia K.

doi:10.1109/tmtt.2016.2638428

Cited by 30 publications

(14 citation statements)

References 23 publications

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“…The contrast

is related to the differential scattering matrix

, measured at the antenna ports, that is the difference between the scattering matrices measured at

and

time instants, respectively. The generic entry

of this matrix can be written as

where the symbol “·” denotes the dot product between vectors, j is the imaginary unit,

is the angular frequency, and

and

are the known incoming root-power waves at the p and q antenna ports, respectively [ 28 , 29 ].

and

are the electric fields radiated in D by the antenna in

and by the antenna in

, respectively.…”

Section: Methodsmentioning

confidence: 99%

Experimental Validation of a Microwave System for Brain Stroke 3-D Imaging

et al. 2021

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This paper experimentally validates the capability of a microwave prototype device to localize hemorrhages and ischemias within the brain as well as proposes an innovative calibration technique based on the measured data. In the reported experiments, a 3-D human-like head phantom is considered, where the brain is represented either with a homogeneous liquid mimicking brain dielectric properties or with ex vivo calf brains. The microwave imaging (MWI) system works at 1 GHz, and it is realized with a low-complexity architecture formed by an array of twenty-four printed monopole antennas. Each antenna is embedded into the “brick” of a semi-flexible dielectric matching medium, and it is positioned conformal to the head upper part. The imaging algorithm exploits a differential approach and provides 3-D images of the brain region. It employs the singular value decomposition of the discretized scattering operator obtained via accurate numerical models. The MWI system analysis shows promising reconstruction results and extends the device validation.

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“…The contrast

is related to the differential scattering matrix

, measured at the antenna ports, that is the difference between the scattering matrices measured at

and

time instants, respectively. The generic entry

of this matrix can be written as

where the symbol “·” denotes the dot product between vectors, j is the imaginary unit,

is the angular frequency, and

and

are the known incoming root-power waves at the p and q antenna ports, respectively [ 28 , 29 ].

and

are the electric fields radiated in D by the antenna in

and by the antenna in

, respectively.…”

Section: Methodsmentioning

confidence: 99%

Experimental Validation of a Microwave System for Brain Stroke 3-D Imaging

et al. 2021

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“…Note, however, that most microwave measurement systems acquire the scattering parameters (Sparameters) instead of electric-field values. As shown in [31], Eq. (2) can be modified to operate using the scattering component of the S-parameter:…”

Section: Linearized Models Of Scatteringmentioning

confidence: 97%

“…In tissue measurements, the differences between Eqs. (16) and (31) typically leads to a larger number of frequency measurements than the maximum number of linearly independent z -plane measurements. For example, consider a measurement in the imaging of a compressed breast tissue of a thickness of 5 cm.…”

Section: Inversion Proceduresmentioning

confidence: 99%

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Comparative Study of the Rytov and Born Approximations in Quantitative Microwave Holography

Tajik¹,

Pitcher²,

Nikolova³

2017

PIER B

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Quantitative microwave holography is a recent imaging methodology that shows promise in medical diagnostics. It is a real-time direct inversion algorithm that reconstructs the complex permittivity from S-parameter measurements on an acquisition surface outside of the imaged object. It is recognized that this imaging method suffers from limitations in tissue imaging due to a forward model which linearizes a highly nonlinear scattering problem. It is therefore important to study its limitations when reconstruction is aided by certain pre-and post-processing filters which are known to improve the image quality. The impact of filtering on the quantitative result is particularly important. In this work, the reconstruction equations of quantitative microwave holography are derived from first principles. The implementation of two linearizations strategies, Born's approximation and Rytov's approximation, is explained in detail in the case of a scattering model formulated in terms of S-parameters. Furthermore, real-space and Fourier-space filters are developed to achieve the best performance for the given linearized model of scattering. Simulated and experimental results demonstrate the limitations of the method and the necessity of filtering. The two approximations are also compared in experimental tissue reconstructions.

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“…Wide-bandwidth frequency sweeps are used as they improve the spatial resolution [5]. The forward model of scattering in terms of S-parameter data is given by [5], [30]:…”

Section: Forward Model Of Scatteringmentioning

confidence: 99%

Real-Time Microwave Imaging of a Compressed Breast Phantom With Planar Scanning

Tajik¹,

Foroutan²,

Shumakov

et al. 2018

IEEE J. Electromagn. RF Microw. Med. Biol.

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Two real-time reconstruction algorithms, i.e., quantitative microwave holography and scattered-power mapping, have been shown to be successful in the imaging of compressed tissue of relatively small thicknesses such as 1 and 2 cm. In both cases, planar data acquisition of frequency-swept transmission coefficients has been employed. Despite the fact that these algorithms are based on a linear forward model of scattering, they have been capable of providing quantitative estimates of the tissue permittivity due to the experimentally derived kernel of the scattering integral. Here, we demonstrate similar performance with a thicker (approximately 5 cm) compressed-breast phantom. This thickness is greater than or comparable to the median thickness employed in mammography, depending on the view (craniocaudal or mediolateral oblique). The two methods are described in a common mathematical framework for the first time. The importance of the system calibration and the choice of a host medium are discussed through experiments. A new method for focusing onto suspect regions is demonstrated. The limitations of real-time imaging are highlighted, along with an outlook to improve the image resolution and suppressing artifacts without sacrificing the reconstruction speed. Future work aims at validation with high complexity, realistic compressed-breast phantoms.

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Frequency-Domain Integral Equations of Scattering for Complex Scalar Responses

Cited by 30 publications

References 23 publications

Experimental Validation of a Microwave System for Brain Stroke 3-D Imaging

Experimental Validation of a Microwave System for Brain Stroke 3-D Imaging

Comparative Study of the Rytov and Born Approximations in Quantitative Microwave Holography

Real-Time Microwave Imaging of a Compressed Breast Phantom With Planar Scanning

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