Henrik Garde

Ilayda Yaman, Guoda Tian, Martin Larsson et al.

We present a synchronized multisensory dataset for accurate and robust indoor localization: the Lund University Vision, Radio, and Audio (LuViRA) Dataset. The dataset includes color images, corresponding depth maps, inertial measurement unit (IMU) readings, channel response between a 5G massive multiple-input and multiple-output (MIMO) testbed and user equipment, audio recorded by 12 microphones, and accurate six degrees of freedom (6DOF) pose ground truth of 0.5 mm. We synchronize these sensors to ensure that all data is recorded simultaneously. A camera, speaker, and transmit antenna are placed on top of a slowly moving service robot, and 89 trajectories are recorded. Each trajectory includes 20 to 50 seconds of recorded sensor data and ground truth labels. Data from different sensors can be used separately or jointly to perform localization tasks, and data from the motion capture (mocap) system is used to verify the results obtained by the localization algorithms. The main aim of this dataset is to enable research on sensor fusion with the most commonly used sensors for localization tasks. Moreover, the full dataset or some parts of it can also be used for other research areas such as channel estimation, image classification, etc. Our dataset is available at: https://github.com/ilaydayaman/LuViRA_Dataset

Henrik Garde, Stratos Staboulis

In inclusion detection in electrical impedance tomography, the support of perturbations (inclusion) from a known background conductivity is typically reconstructed from idealized continuum data modelled by a Neumann-to-Dirichlet map. Only few reconstruction methods apply when detecting indefinite inclusions, where the conductivity distribution has both more and less conductive parts relative to the background conductivity; one such method is the monotonicity method of Harrach, Seo, and Ullrich. We formulate the method for irregular indefinite inclusions, meaning that we make no regularity assumptions on the conductivity perturbations nor on the inclusion boundaries. We show, provided that the perturbations are bounded away from zero, that the outer support of the positive and negative parts of the inclusions can be reconstructed independently. Moreover, we formulate a regularization scheme that applies to a class of approximative measurement models, including the Complete Electrode Model, hence making the method robust against modelling error and noise. In particular, we demonstrate that for a convergent family of approximative models there exists a sequence of regularization parameters such that the outer shape of the inclusions is asymptotically exactly characterized. Finally, a peeling-type reconstruction algorithm is presented and, for the first time in literature, numerical examples of monotonicity reconstructions for indefinite inclusions are presented.

Henrik Garde

Detecting inhomogeneities in the electrical conductivity is a special case of the inverse problem in electrical impedance tomography, that leads to fast direct reconstruction methods. One such method can, under reasonable assumptions, exactly characterize the inhomogeneities based on monotonicity properties of either the Neumann-to-Dirichlet map (non-linear) or its Fréchet derivative (linear). We give a comparison of the non-linear and linear approach in the presence of measurement noise, and show numerically that the two methods give essentially the same reconstruction in the unit disk domain. For a fair comparison, exact matrix characterizations are used when probing the monotonicity relations to avoid errors from numerical solution to PDEs and numerical integration. Using a special factorization of the Neumann-to-Dirichlet map also makes the non-linear method as fast as the linear method in the unit disk geometry.

Henrik Garde, Kim Knudsen

This paper focuses on prior information for improved sparsity reconstruction in electrical impedance tomography with partial data, i.e. data measured only on subsets of the boundary. Sparsity is enforced using an $\ell_1$ norm of the basis coefficients as the penalty term in a Tikhonov functional, and prior information is incorporated by applying a spatially distributed regularization parameter. The resulting optimization problem allows great flexibility with respect to the choice of measurement boundaries and incorporation of prior knowledge. The problem is solved using a generalized conditional gradient method applying soft thresholding. Numerical examples show that the addition of prior information in the proposed algorithm gives vastly improved reconstructions even for the partial data problem. The method is in addition compared to a total variation approach.

Henrik Garde, Kim Knudsen

In electrical impedance tomography the electrical conductivity inside a physical body is computed from electro-static boundary measurements. The focus of this paper is to extend recent result for the 2D problem to 3D. Prior information about the sparsity and spatial distribution of the conductivity is used to improve reconstructions for the partial data problem with Cauchy data measured only on a subset of the boundary. A sparsity prior is enforced using the $\ell_1$ norm in the penalty term of a Tikhonov functional, and spatial prior information is incorporated by applying a spatially distributed regularization parameter. The optimization problem is solved numerically using a generalized conditional gradient method with soft thresholding. Numerical examples show the effectiveness of the suggested method even for the partial data problem with measurements affected by noise.