Branko Kolundzija

One of the main challenges in medical microwave imaging is to provide meaningful images when only minimal a priori information is available. Concerning the case of brain stroke imaging, this paper proposes a novel method for generating a low-resolution patient-specific approximation of the head by processing the same data used for the diagnosis. The method assumes knowledge of the head shape and a rough approximation of the fat and skin tissue above the skull. The approach consists of two steps. First, the measured data are processed using the first-order Born approximation scattering model to generate a qualitative head image. The underlying linear inverse problem is regularized by representing the unknown complex permittivity in terms of Chebyshev polynomials to improve its stability and effectiveness. Then, the voxels belonging to the skull are identified in the obtained image, and the skull boundaries are approximated from the discrete data using spherical harmonics. The proposed method is tested against an anthropomorphic phantom, demonstrating its capability to derive a patient-specific approximation. Moreover, the obtained background model enables stroke detection using real-time qualitative imaging.

A simple, robust, and easy-to-implement method is considered for verification of homogenous half-space dyadic Green’s matrices (DGMs) that relate electric and magnetic fields to elementary current sources placed near an infinite ground plane. The DGMs, as a rule, are calculated using either the Sommerfeld integrals or their approximations. The verification is based on an alternative method for evaluation of DGMs, in which elementary current sources are modeled by electrically small antennas and the infinite ground plane is modeled by a finite-sized piece of ground, i.e. the ground clump. The method is demonstrated by using a typical 3-D EM solver based on the method-of-moments (MoM) solution of surface integral equations (SIEs). The single-antenna scenario is proved effective for obtaining results with controllable accuracy, with relative error going from 10-2 to 10-5, which is demonstrated for ground clumps up to 20λ in diameter. A set of three electric and three magnetic dipoles is recommended for fast verification of DGMs.

A multi-epoch mini-batch variant of the Levenberg-Marquardt algorithm (LMA) is proposed for an efficient training of large training sets applied in consensus deep neural network (Consensus DNN) of complex antenna models. In each training epoch the proposed approach divides whole training set into mini-batches and applies multiple iterations on each of them, where initial weights and biases are overtaken from the previously trained mini-batch. By appropriately selecting the mini-batch size and number of iterations per mini-batch, the adapted LMA enables shorter training time and higher accuracy than standard LMA. Owing to this adaptation the training of Consensus DNN is facilitated and its accuracy is improved.

Entire set of expressions for components of reflected and transmitted EM fields in a lossy dielectric half-space scenario, excited by an elementary electric-current Hertz dipole, is presented in form of magnetic vector-potential Green's functions. Theoretically, by substituting appropriately the dual magnitudes - magnetic with electric vector-potential, and dielectric permittivity with magnetic permeability, dual equations can be derived for magnetic-current excitation. This claim is verified by means of a commercial general-purpose MoM solver based on surface integral equations.

We developed a novel qualitative imaging algorithm based on a polynomial approximation of the unknown contrast and sparse ( l ₁ ) regularization. Contrary to previously published results, we defined polynomial basis functions on subdomains that divide the investigation domain. Moreover, we formulated constraints that ensure the continuity of the contrast on subdomain borders. We showed that the proposed algorithm improved imaging resolution, particularly in multiple target scenarios. We demonstrated that partitioning the investigation domain together with contrast continuity formulation enhanced the numerical stability and reduced the computation time. The obtained results were significantly less sensitive to the regularization parameter values than those obtained using the standard polynomial approximation. Namely, smaller domains allow lower polynomial orders, which are numerically more favorable. Continuity constraints reduce the search space and mitigate the occurrence of false solutions. Another contribution of this study is a novel strategy for regularization parameter selection. We considered different figures of merit and numerical scenarios to study the influence of various parameters involved in the imaging process, such as the polynomial order and number of subdomains. An extensive analysis proved the robustness of the approach against noise. The proposed algorithm was designed for two-dimensional geometry. However, generalization to three-dimensional space is straightforward. The algorithm can also be used with other types of regularization such as the l ₂ regularization. Potential applications include medical microwave imaging, in which high resolution and noise immunity are vital features.