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In this work we present a systematic evaluation of the potential of combining dielectric materials with an array of electric dipoles for MRI. Design parameters include the permittivity and length of a dielectric sleeve, as well as the dipole length and position of the tuning inductors. Results show that the combined approach improves transmit efficiency and SNR by ∼10 to 15 % compared to an optimized...
In this paper, we present an Electrical Properties Tomography (EPT) methodology based on integral (Green's tensor) representations for the electromagnetic field. Inhomogeneous tissue profiles can easily be incorporated in such an approach and the reconstruction method is less sensitive to noise compared with more standard differential based EPT methods since smoothing integral operators act on measured...
In this paper we present a structure-preserving model-order reduction technique to efficiently compute electromagnetic wave fields on unbounded domains. As an approximation space, we take the span of the real and imaginary parts of frequency-domain solutions of Maxwell's equations. Reduced-order models for the electromagnetic field belong to this space and the expansion coefficients of these models...
High-field MRI reduces the homogeneity of the B1+ transmit field, which in turn degrades the quality of MR images. High-permittivity pads are increasingly used to restore the homogeneity of this transmit field. Designing such a pad in terms of dimensions, position, and constitution is not trivial, however, and in this work we propose a design method that can be used to find an optimal pad for a certain...
In this paper we demonstrate the effectiveness of Krylov subspace model-order reduction techniques to simulate wave field propagation in strongly resonating structures. By utilizing an optimal complex-scaling method that simulates the extension to infinity, we show that Krylov reduction allows for effective wave field computations and dominant open resonant modes can be obtained at negligible additional...
We present a Krylov subspace projection framework to model electromagnetic wave propagation in unbounded domains. The extension to infinity is modeled via an optimal complex scaling method and we show that stable time-domain reduced-order models can be efficiently computed via a stability-correction procedure in conjunction with a Lanczos-type reduction algorithm. We show that dominant open resonant...
In this paper, we consider so-called optimal circulant preconditioners for discretized integral operators describing the scattering of steady state electromagnetic waves by penetrable objects embedded in homogeneous background media. For two-dimensional scattering problems, we show that the preconditioners may significantly increase the convergence rate of an iterative solver. Possible extensions...
In this paper, we present a novel method (Contrast Source Inversion — Electric Properties Tomography or CSI-EPT) to dielectric imaging of biological tissue using so-called B1+ data measurable by Magnetic Resonance Imaging (MRI) systems. Integral representations for the electromagnetic field quantities are taken as a starting point and we follow an iterative contrast source inversion approach to retrieve...
We present a modified Newton minimization scheme for two-parameter inversion problems. Starting point is a so-called reduced-order objective function which measures the discrepancy between measured data and model-order reduction scattered field data. This objective function is minimized on a specified range of permittivity and conductivity values and a nonlinear transformation turns this constraint...
In this paper, we present an optimal circulant preconditioner for domain integral equations in electromagnetics. The preconditioner is the best circulant fit to the discretized domain integral operator as measured by the Frobenius norm. We show that the discretized integral operators exhibit a Toeplitz-like structure for inhomogeneous objects and present an explicit expression for the elements of...
In this paper we consider a three-dimensional electromagnetic field in a homogeneous and time-variant medium. After a spatial Fourier transformation we solve Maxwell's equations for the electric and magnetic flux densities and write the solution in terms of the so-called transition matrix. This matrix can be given in terms of the well known Peano-Baker series and we show that in the constant impedance...
In this paper we show that the Finite-Difference Time-Domain method (FDTD method) follows the recurrence relation for Fibonacci polynomials. This observation allows us to easily derive the Courant-Friedrichs-Lewy stability condition by exploiting the connection between Fibonacci polynomials and Chebyshev polynomials of the second kind. In addition, we compare FDTD with the Spectral Lanczos Decomposition...
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