Bert Jan Kooij

THE RETRIEVAL OF A BURIED CYLINDRICAL OBSTACLE BY A CONSTRAINED MODIFIED GRADIENT METHOD IN THE H-POLARIZATION CASE AND FOR MAXWELLIAN MATERIALS

The retrieval of an unknown, possibly inhomogeneous, penetrable cylindrical obstacle buried entirely in a known homogeneous half-space - the constitutive material parameters of the obstacle and of its embedding obey a Maxwell model - is considered from single- or multiple-frequency aspect-limited data collected by ideal sensors located in air above the embedding half-space, when a small number of time-harmonic transverse electric (TE)-polarized line sources - the magnetic field H is directed along the axis of the cylinder - is also placed in air. The wavefield is modelled from a rigorous H-field domain integral-differential formulation which involves the dot product of the gradients of the single component of H and of the Green function of the stratified environment times a scalar-valued contrast function which contains the obstacle parameters (the frequency-independent, position-dependent relative permittivity and conductivity). A modified gradient method is developed in order to reconstruct the maps of such parameters within a prescribed search domain from the iterative minimization of a cost functional which incorporates both the error in reproducing the data and the error on the field built inside this domain. Non-physical values are excluded and convergence reached by incorporating in the solution algorithm, from a proper choice of unknowns, the condition that the relative permittivity be larger than or equal to 1, and the conductivity be non-negative. The efficiency of the constrained method is illustrated from noiseless and noisy synthetic data acquired independently. The importance of the choice of the initial values of the sought quantities, the need for a periodic refreshment of the constitutive parameters to avoid the algorithm providing inconsistent results, and the interest of a frequency-hopping strategy to obtain finer and finer features of the obstacle when the frequency is raised, are underlined. It is also shown that though either the permittivity map or the conductivity map can be obtained for a fair variety of cases, retrieving both of them may be difficult unless further information is made available.

Increasing signal homogeneity and image quality in abdominal imaging at 3 T with very high permittivity materials

The appearance of severe signal drop‐outs in abdominal imaging at 3 T arises primarily from areas of very low B  1+ transmit field in the body, and is problematic in both obese as well as very thin subjects. In this study, we show how thin patient‐friendly pads containing new high permittivity materials can be designed and optimized, and when placed around the subject increase substantially the B  1+ uniformity and the image quality. Results from nine healthy volunteers show that inclusion of these dielectric pads results in statistically significant decreases in the coefficient of variance of the B  1+ field, with stronger and more uniform fields being produced. In addition there are statistically significant decreases in time‐averaged power required for scanning. These differences are present in both quadrature‐mode operation (coefficient of variance decrease, P < 0.0001, mean 25.4 ± 10%: power decrease, P = 0.005, mean 14 ± 14%) and also for the RF‐shimmed case (coefficient of variance decrease, P = 0.01, mean 16 ± 13%: power decrease, P = 0.005, mean 22 ± 11%) of a dual‐transmit system. Magn Reson Med, 2012.

Nonlinear inversion in TE scattering

A method for reconstructing the complex permittivity of a bounded inhomogeneous object from measured scattered-field data is presented. This paper extends the method previously developed for the TM case to the more complicated TE case. In the TM case, the electric-field integral equation involves an integral operator whose integrand was simply a product of the background Greens function, contrast, and field. In the TE case, the magnetic field is polarized along the axis of an inhomogeneous cylinder of arbitrary cross section and the corresponding integral equation contains derivatives of both the background Greens function and the field. The nonlinear inversion based upon the modified-gradient method as presented in the literature is applied to the magnetic-field equation. However, the integral equation can also be formulated as an electric-field integral equation for the two transversal components of the electric field. Again, the integrand is a product of the background Greens function, contrast, and electric-field vector. The derivatives are operative outside the integral. In this paper, the latter formulation will be taken as a point of departure to develop a nonlinear inversion scheme using the modified-gradient method.

The traveling point load revisited

Abstract The nonaxisymmetrical boundary value problem of a point load of normal traction traveling over an elastic halfspace is revisited. The transient problem was first solved in the space-time domain in a paper by D.C. Gakenheimer and J. Miklowitz [Transient excitation of an elastic half space by a point load traveling on the surface, J. Appl. Mech. 36 (1969) 505–515] who used a modified Cagniard technique. As compared to this original work, the analysis in the present paper is more straightforward, thus allowing more insight into this important canonical problem. Some procedural matters in the analysis are set straight. Theoretical wavefronts are shown for each sonic load speed and, moreover, numerical results are presented for transonic and supersonic load motion.

Assessing the MR compatibility of dental retainer wires at 7 tesla

To determine the MR compatibility of common dental retainer wires at 7 Tesla in terms of potential RF heating and magnetic susceptibility effects.

Nonlinear inversion of a buried object in transverse electric scattering

A method for reconstructing the material properties of a buried bounded inhomogeneous object from measured scattered field data at the surface of the Earths interface is presented. This work extends the method previously developed for the homogeneous transverse electric (TE) case to the more complicated case of a buried object. In the TE case, the magnetic field is polarized along the axis of an inhomogeneous cylinder of arbitrary cross section, and the corresponding integral equation contains derivatives of both the background Greens function and the field. The nonlinear inversion, however, can be formulated from an electric field integral equation for the two transversal components of the electric field. The integrand is a product of the background Greens function, the contrast, and the electric field vector; however, in the case of a buried object the background Greens function is the one pertaining to a two-media configuration. The derivatives are operative outside the integral. In this paper the latter formulation will be taken as the point of departure to develop a nonlinear inversion scheme based upon the modified gradient method. In the inversion scheme the positivity of the material parameters has to be ensured in order to obtain a convergent inversion scheme. Numerical results are presented in which the reconstruction of the contrast is shown and compared in the case of TE excitation as well as transverse magnetic (TM) excitation.

Impulsive sound reflection from an absorptive and dispersive planar boundary

The impulsive sound reflection from a planar boundary with absorptive and dispersive properties is investigated. The acoustic properties of the boundary are modeled via a local impedance transfer function whose complex frequency domain representation is taken to be a Pade (2,2) expression. The coefficients in this representation are matched to frequency domain acoustic wave reflection measurements. With the aid of the Cagniard–De Hoop method, a closed-form space-time expression is derived for the acoustic pressure of the reflected wave arising from the incidence of a point-source monopole excited spherical pulse. Depending on the acoustic impedance properties of the boundary, large-amplitude oscillating surface effects can occur. These surface phenomena differ in nature from the true surface waves like the Rayleigh, Scholte, and Stoneley waves in elastodynamics. Illustrative numerical results are presented.

Image reconstruction from Ipswich data. III

For pt.II see ibid., vol.39, p.29-32 (1997). We describe results obtained in image reconstruction using the Ipswich data sets IPS009-IPS012. In van den Berg et al. (1995, 1997) and van den Berg and Kleinman (1996), we employed versions of the modified gradient method to reconstruct the shape, location, and index of refraction of known and unknown scatterers, both dielectric and perfectly conducting, from the measured scattered field data contained in IPS001-IPS008. In the present paper, we employ a new inversion method, the contrast source inversion (CSI) method, for the reconstructions. We include here a brief description of the method, given in greater detail in van den Berg and Kleinman. In the case of the new Ipswich experiments, we have 36 angles of incidence, equidistantly distributed around the object. The unknown scatterer is assumed to be located somewhere in a known, bounded, test domain D (taken to be square), and the scattered field is measured on a domain S (taken to be a circle) containing the test domain D in its interior. In the case of the Ipswich experiments, S was taken to be in the far zone of the scattered field, and measurements were made at 18 angles of observation, equidistantly distributed over a semicircle. For each experiment, this semicircle started with the forward-scattering angle.

Parametrization of acoustic boundary absorption and dispersion properties in time-domain source/receiver reflection measurement

Closed-form analytic time-domain expressions are obtained for the acoustic pressure associated with the reflection of a monopole point-source excited impulsive acoustic wave by a planar boundary with absorptive and dispersive properties. The acoustic properties of the boundary are modeled as a local admittance transfer function between the normal component of the particle velocity and the acoustic pressure. The transfer function is to meet the conditions for linear, time-invariant, causal, passive behavior. A parametrization of the admittance function is put forward that has the property of showing up explicitly, and in a relatively simple manner, in the expression for the reflected acoustic pressure. The partial fraction representation of the complex frequency domain admittance is shown to have such a property. The result opens the possibility of constructing inversion algorithms that enable the extraction of the relevant parameters from the measured time traces of the acoustic pressure at different offsets, parallel as well as normal to the boundary, between source and receiver. Illustrative theoretical numerical examples are presented.

The transient electromagnetic field of an electric line source above a plane conducting earth

The pulsed electromagnetic radiation from an electric line source above a conducting earth is investigated theoretically. The modified Cagniard method is used to derive closed-form expressions for the electric and magnetic field anywhere above the conducting earth. Numerical results are presented for the electric field for different points of excitation and observation above the earth, as well as for different values of the earths material parameters, i.e. permittivity and electrical conductivity. It is shown that the effect of the conductivity is of significant importance to the calculation of interfering transient electromagnetic fields in the presence of a conducting earth. >