arXiv subjects

N. Hyvönen

Publications and source records attributed to N. Hyvönen.

4 recordsLinked to original sources

arXiv2026

Total variation regularization with reduced basis in electrical impedance tomography

This work considers using reduced basis techniques in connection to (smoothened) total variation regularization in electrical impedance tomography, but analogous ideas can also be used for other inverse elliptic boundary value problems. It is demonstrated that resorting to reduced bases can speed up a reconstruction algorithm based on combining the lagged diffusivity algorithm with sequential linearizations and preconditioned LSQR iteration without any significant loss of reconstruction quality or of the edge-enhancing nature of total variation regularization. The ideas are numerically tested in three dimensions on unstructured finite element meshes with both simulated and experimental data, resulting in online reconstruction times of only a few seconds on a standard laptop computer.

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arXiv2026

Local electrical impedance tomography via projections

This paper introduces a method for approximately eliminating the effect that conductivity changes outside the region of interest have in electrical impedance tomography, allowing to form a local reconstruction in the region of interest only. The method considers the Jacobian matrix of the forward map, i.e., of the map that sends the discretized conductivity to the electrode measurements, at an initial guess for the conductivity. The Jacobian matrix is divided columnwise into two parts: one corresponding to the region of interest and a nuisance Jacobian corresponding to the rest of the domain. The leading idea is to project both the electrode measurements and the forward map onto the orthogonal complement of the span of a number of left-hand singular vectors for a suitably weighted nuisance Jacobian. The weighting can, e.g., account for the element sizes in a finite element discretization or to prior information on the conductivity outside the region of interest. The inverse problem is then solved by considering the projected relation between the measurements and the forward map, only reconstructing the conductivity in the region of interest. The functionality of the method is demonstrated by applying a reconstruction algorithm that combines lagged diffusivity iteration and total variation regularization to experimental data. In particular, data from a head-shaped water tank is considered, with the conductivity change in the region of interest mimicking growth of a hemorrhagic stroke and the changes outside the region of interest imitating physiological variations in the conductivity of the scalp.

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arXiv2023

Bayesian experimental design for head imaging by electrical impedance tomography

This work considers the optimization of electrode positions in head imaging by electrical impedance tomography. The study is motivated by maximizing the sensitivity of electrode measurements to conductivity changes when monitoring the condition of a stroke patient, which justifies adopting a linearized version of the complete electrode model as the forward model. The algorithm is based on finding a (locally) A-optimal measurement configuration via gradient descent with respect to the electrode positions. The efficient computation of the needed derivatives of the complete electrode model is one of the focal points. Two algorithms are introduced and numerically tested on a three-layer head model. The first one assumes a region of interest and a Gaussian prior for the conductivity in the brain, and it can be run offline, i.e., prior to taking any measurements. The second algorithm first computes a reconstruction of the conductivity anomaly caused by the stroke with an initial electrode configuration by combining lagged diffusivity iteration with sequential linearizations, which can be interpreted to produce an approximate Gaussian probability density for the conductivity perturbation. It then resorts to the first algorithm to find new, more informative positions for the available electrodes with the constructed density as the prior.

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arXiv2021

Electrodeless electrode model for electrical impedance tomography

Electrical impedance tomography is an imaging modality for extracting information on the interior structure of a physical body from boundary measurements of current and voltage. This work studies a new robust way of modeling the contact electrodes used for driving current patterns into the examined object and measuring the resulting voltages. The idea is to not define the electrodes as strict geometric objects on the measurement boundary, but only to assume approximate knowledge about their whereabouts and let a boundary admittivity function determine the actual locations of the current inputs. Such an approach enables reconstructing the boundary admittivity, i.e. the locations and strengths of the contacts, at the same time and with analogous methods as the interior admittivity. The functionality of the new model is verified by two-dimensional numerical experiments based on water tank data.

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