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Synthetic-aperture (SA) imaging is a popular method to visualize the reflectivity of an object from ultrasonic reflections. The method yields an image of the (volume) contrast in acoustic impedance with respect to the embedding. Typically, constant mass density is assumed in the underlying derivation. Due to the band-limited nature of the recorded data, the image is blurred in space, which is quantified by the associated point spread function. SA volume imaging is valid under the Born approximation, where it is assumed that the contrast is weak. When objects are large with respect to the wavelength, it is questionable whether SA volume imaging should be the method-of-choice. Herein, we propose an alternative solution that we refer to as SA interface imaging. This approach yields a vector image of the discontinuities of acoustic impedance at the tissue interfaces. Constant wave speed is assumed in the underlying derivation. The image is blurred in space by a tensor, which we refer to as the interface spread function. SA interface imaging is valid under the Kirchhoff approximation, where it is assumed that the wavelength is small compared to the spatial dimensions of the interfaces. We compare the performance of volume and interface imaging on synthetic data and on experimental data of a gelatin cylinder with a radius of 75 wavelengths, submerged in water. As expected, the interface image peaks at the gelatin-water interface, while the volume image exposes a peak and trough on opposing sides of the interface.

In this work, an iterative inversion algorithm for deblurring and deconvolution is considered. The algorithm is based on the conjugate gradient scheme and uses the so-called weighted L2-norm regularizer to obtain a reliable solution. The regularizer is included as a multiplicative constraint. In this way, the appropriate regularization parameter will be controlled by the optimization process itself. In fact, the misfit in the error in the space of the blurring operator is the regularization parameter. Then, no a priori knowledge on the blurred data or image is needed. If noise is present, the misfit in the error consisting of the blurring operator will remain at a large value during the optimization process; therefore, the weight of the regularization factor will be more significant. Hence, the noise will, at all times, be suppressed in the reconstruction process. Although one may argue that, by including the regularization factor as a multiplicative constraint, the linearity of the problem has been lost, careful analysis shows that, under certain restrictions, no new local minima are introduced. Numerical testing shows that the proposed algorithm works effectively and efficiently in various practical applications.

The total variation minimization method for deblurring noise is shown to be effective in increasing the resolution in a contrast source inversion approach to index reconstruction from measured scattered field data. The main drawback is the presence of an artificial weighting parameter in the cost functional, which can only be determined through considerable experimentation Therefore, we introduce the total variation as a multiplicative constraint. Numerical examples demonstrate that the algorithm based on this multiplicative regularization seems to be robust and handling noisy data very well without the necessity of the weighting parameter.

An efficient iterative method for solving quasi-static electromagnetic field problems is presented. The electromagnetic field is generated by an inductive applicator and is represented as a superposition of two constituents, viz. a primary field in absence of the tissue configuration and a secondary field generated by the presence of the tissue. Then, for the secondary field a quasi-static approximation is employed. In the quasi-static field equations a relaxation function is introduced, such that the resulting equations can be solved iteratively. For a realistic three-dimensional model of a human hand numerical results are presented.

An efficient iterative method for solving quasi-static electromagnetic field problems is presented. A relaxation function is introduced in the quasi-static field equations. Then, the resulting equations can be solved by iteration. The method is similar to the one of solving a Laplace equation by computing the stationary state of a diffusion equation. Next, for a radially layered configuration the numerical results are compared with the results from an existing integral equation method. Subsequently, for a realistic three-dimensional model of a human knee numerical results are arrived at.

The electromagnetic heat dissipation in a radially layered biological tissue inside a ring capacitor (RC) applicator has been investigated. A quasi-static model is introduced to compute the relevant electromagnetic field quantities. The method of computation employs the spatial Fourier transform of all field quantities with respect to the axial coordinate. After an iterative solution of a dual boundary value problem for the electric potential and the current density at the electrodes, an inverse Fourier transform is carried out to compute the quantities that are of interest to the deep-body system at hand. Comparison of numerical results with phantom measurements shows excellent agreement.