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We investigate the Helmholtz equation in a two dimensional open waveguide with a thin and high contrast core layer. We develop an asymptotic analysis of the Green function of the problem, and through it we identify and characterize the…
The brain cortex, which processes visual, auditory and sensory data in the brain, is known to have many recurrent connections within its layers and from higher to lower layers. But, in the case of machine learning with neural networks, it…
The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and…
In Acousto-Electric tomography, the objective is to extract information about the interior electrical conductivity in a physical body from knowledge of the interior power density data generated from prescribed boundary conditions for the…
The task of person re-identification has recently received rising attention due to the high performance achieved by new methods based on deep learning. In particular, in the context of video-based re-identification, many state-of-the-art…
Electrical Impedance Tomography (EIT) is a powerful imaging technique with diverse applications, e.g., medical diagnosis, industrial monitoring, and environmental studies. The EIT inverse problem is about inferring the internal conductivity…
In this paper, we present a new algorithm for computing the linear recurrence relations of multi-dimensional sequences. Existing algorithms for computing these relations arise in computational algebra and include constructing structured…
We consider the imaging of anisotropic conductivity tensors $\gamma=(\gamma_{ij})_{1\leq i,j\leq 2}$ from knowledge of several internal current densities $\mathcal{J}=\gamma\nabla u$ where $u$ satisfies a second order elliptic equation…
The method of flow tracing follows the power flow from net-generating sources through the network to the net-consuming sinks, which allows to assign the usage of the underlying transmission infrastructure to the system participants. This…
The image reconstruction problem of the tomographic imaging technique magnetic particle imaging (MPI) requires the solution of a linear inverse problem. One prerequisite for this task is that the imaging operator that describes the mapping…
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…
The goal of this article is to study fundamental mechanisms behind so-called indirect and direct data-driven control for unknown systems. Specifically, we consider policy iteration applied to the linear quadratic regulator problem. Two…
Inversion of gravity data is an important method for investigating subsurface density variations relevant to mineral exploration, geothermal assessment, carbon storage, natural hydrogen, groundwater resources, and tectonic evolution. Here…
We consider the inverse problem of reconstructing an unknown function $u$ from a finite set of measurements, under the assumption that $u$ is the trajectory of a transport-dominated problem with unknown input parameters. We propose an…
Magnetic resonance imaging (MRI) is a versatile imaging technique that allows different contrasts depending on the acquisition parameters. Many clinical imaging studies acquire MRI data for more than one of these contrasts---such as for…
The inverse scattering problems have been popular for the past thirty years. While very successful in many cases, progress has lagged when only {\em limited-aperture} measurement is available. In this paper, we perform some elementary study…
We study the inverse problem of reconstructing an incompressible velocity field $\boldsymbol{v}$ from observations of the induced magnetic field $\boldsymbol{b}$. In the presence of a strong, constant background field $\mathbf{F}$, the…
This paper is concerned with the inverse problem of reconstructing an inhomogeneous medium from the acoustic far-field data at a fixed frequency in two dimensions. This inverse problem is severely ill-posed (and also strongly nonlinear),…
The motivation of this work is an inverse problem for the acoustic wave equation, where an array of sensors probes an unknown medium with pulses and measures the scattered waves. The goal of the inversion is to determine from these…
We consider the inverse problem of the simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions of the Maxwell's system in 3D with limited boundary observations of the electric field. The theoretical…