Magnetic fields are often utilized for position sensing of mobile devices. In typical sensing systems, multiple sensors are used to detect magnetic fields generated by target devices. To determine the positions of the devices, magnetic-field data detected by the sensors must be converted to device-position data. The data conversion is not trivial because it is a nonlinear inverse problem. In this study, we propose a machine-learning approach suitable for data conversion required in the magnetic-field-based position sensing of target devices. In our approach, two different sets of training data are used. One of the training datasets is composed of raw data of magnetic fields to be detected by sensors. The other set is composed of logarithmically represented data of the fields. We can obtain two different predictor functions by learning with these training datasets. Results show that the prediction accuracy of the target position improves when the two different predictor functions are used. Based on our simulation, the error of the target position estimated with the predictor functions is within 10cm in a 2m × 2m × 2m cubic space for 87% of all the cases of the target device states. The computational time required for predicting the positions of the target device is 4ms. As the prediction method is accurate and rapid, it can be utilized for the real-time tracking of moving objects and people.

Convolutional approximate message-passing (CAMP) is an efficient algorithm to solve linear inverse problems. CAMP aims to realize advantages of both approximate message-passing (AMP) and orthogonal/vector AMP. CAMP uses the same low-complexity matched-filter as AMP. To realize the asymptotic Gaussianity of estimation errors for all right-orthogonally invariant matrices, as guaranteed in orthogonal/vector AMP, the Onsager correction in AMP is replaced with a convolution of all preceding messages. CAMP was proved to be asymptotically Bayes-optimal if a state-evolution (SE) recursion converges to a fixed-point (FP) and if the FP is unique. However, no proofs for the convergence were provided. This paper presents a theoretical analysis for the convergence of the SE recursion. Gaussian signaling is assumed to linearize the SE recursion. A condition for the convergence is derived via a necessary and sufficient condition for which the linearized SE recursion has a unique stationary solution. The SE recursion is numerically verified to converge toward the Bayes-optimal solution if and only if the condition is satisfied. CAMP is compared to conjugate gradient (CG) for Gaussian signaling in terms of the convergence properties. CAMP is inferior to CG for matrices with a large condition number while they are comparable to each other for a small condition number. These results imply that CAMP has room for improvement in terms of the convergence properties.

This paper provides a review on the optimal design of photonic bandgap structures by inverse problem techniques. An overview of inverse problems techniques is given, with a special focus on topology design methods. A review of first applications of inverse problems techniques to photonic bandgap structures and waveguides is given, as well as some model problems, which provide a deeper insight into the structure of the optimal design problems.

Generalized Pulse Spectrum Technique (GPST) is a method to solve the inverse problems of wave-propagation and diffusion-dominated phenomena, and therefore has been popularly applied in image reconstruction of time-resolved diffuse optical tomography. With a standard GPST for simultaneous reconstruction of absorption and scattering coefficients, the products of the gradients of the Green's function and the photon-density flux, based on the photon-diffusion equation, are required to calculate the diffusion-related Jacobian matrix. The adversities are of two-folds: time-consuming and singular in the field near the source. The latter causes a severe insensitivity of the algorithm to the scattering changes deep inside tissue. To cope with the above difficulties, we propose in this paper a modified GPST algorithm that only involves the Green's function and the photon-density flux themselves in the scattering-related matrix. Our simulated and experimental reconstructions show that the modified algorithm can significantly improve the quality of scattering image and accelerate the reconstruction process, without an evident degradation in absorption image.

This paper deals with a quantitative inversion algorithm for reconstructing the permittivity and conductivity profiles of bounded inhomogeneous buried objects from measured multifrequency and multiincidence backscattered field data. An Edge-Preserving regularization scheme is applied leading to a significant enhancement in the profiles reconstructions. The applications concern civil engineering and geophysics as well as mine detection and localization. The performance of the reconstructions are illustrated with different synthetic data.

Retrieving the unknown parameters of scattering objects from measured field data is the subject of microwave imaging. This is naturally and usually posed as an optimization problem. In this paper, micro genetic algorithm coupled with deterministic method is applied to the shape reconstruction of perfectly conducting cylinders. The combined approach, with a very small population like the micro genetic algorithm, performs much better than the conventional large population genetic algorithms (GA's) in reaching the optimal region. In addition, we propose a criterion for switching the micro GA to the deterministic optimizer. The micro GA is utilized to effectively locate the vicinity of the global optimum, while the deterministic optimizer is employed to efficiently reach the optimum after inside this region. Therefore, the combined approach converges to the optimum much faster than the micro GA. The proposed approach is first tested by a function optimization problem, then applied to reconstruct perfectly conducting cylinders from both synthetic data and real data. Impressive and satisfactory results are obtained for both cases, which demonstrate the validity and effectiveness of the proposed approach.

It is shown from the Hilberts theory that if the real function Π(θ) has no zeros over the interval [0, 2π], it can be factorized into a product of the factor π+(θ) and its complex conjugate π-(θ)(=). This factorization is tested to decompose a real far-zone field pattern having zeros. To this end, the factorized factors are described in terms of bicomplex mathematics. In our bicomplex mathematics, the temporal imaginary unit "j" is newly defined to distinguish from the spatial imaginary unit i, both of which satisfy i2=-1 and j2=-1.

This paper deals with two different quantitative inversion algorithms for reconstructing the complex permittivity profile of bounded inhomogeneous objects from measured scattered field data. The first algorithm involves an imaging method with single frequency excitation and multiincidence illumination and the second algorithm involves a method with synthetic pulse (multifrequency mode) excitation for objects surrounded by freespace or buried in stratified half-space media. Transmission or reflection imaging protocols are considered depending on aimed applications: microwave imaging in free-space from far-field data for target identification, microwave imaging from near-field data for nondestructive testing (NDT), microwave tomography of buried objects for mine detection and localization, civil engineering and geophysical applications. And Edge-Preserving regularization scheme leading to a significant enhancement in the image reconstructions is also proposed. The methods are illustrated with synthetic and experimental data.

In the present communication we propose the application of unsupervised Artificial Neural Networks (ANN) to solve general ill-posed problems and particularly we apply them to the the estimation of the direction of arrival (DOA) of VLF/ELF radio waves. We use the wave distribution method which consists in the reconstruction of the energy distribution of magnetospheric VLF/ELF waves at the ionospheric base from observations of the wave's electromagnetic field on the ground. The present application is similar to a number of computerized tomography and image enhancement problems and the proposed algorithm can be straightforwardly extended to other applications in which observations are linearly related to unknowns. Then, we have proven the applicability and also we indicate the superiority of the ANN to the conventional methods to handle this kind of problems.