arXiv subjects

Altti Jääskeläinen

Publications and source records attributed to Altti Jääskeläinen.

2 recordsLinked to original sources

arXiv2026

Projections for handling uncertainties and enabling domain truncation in diffuse optical tomography

This paper presents a projection-based technique to mitigate the impact of modeling errors related to domain truncation, changes in the optode coupling coefficients, and misspecified optical parameters of different tissue types in diffuse optical tomography. The approach considers the primary Jacobian matrix of the forward map in the image reconstruction scheme, linking the primary unknown, i.e., the per-voxel absorption coefficient changes in the region of interest, to the optode measurements, as well as the nuisance Jacobians that do the same for the auxiliary unknown parameters of secondary interest. To mitigate mismodeled coupling coefficients or domain truncation, the method projects the linearized forward model defined by the primary Jacobian onto the orthogonal complement of the range of a nuisance Jacobian, or onto the orthogonal complement of the span of a number of first left singular vectors for the nuisance Jacobian that has been weighted to account for prior information on the measurement setup. In the case of a misspecified baseline optical parameter for some tissue type, the nullspace of the utilized orthogonal projection is defined to be the span of first left singular vectors for a (weighted) difference of two Jacobian matrices evaluated at two different levels for the considered tissue-wise optical parameter. The reconstruction is formed by applying Bayesian inversion with Gaussian prior and noise models to the projected linearized equation. We evaluate the method on simulated brain activity data obtained via Monte Carlo simulations of the radiative transfer equation in a voxelized head anatomy for a neonate with combined gestational and chronological age of 41.7 weeks.

math.NA↗

arXiv2024

Projection-based preprocessing for electrical impedance tomography to reduce the effect of electrode contacts

This work introduces a method for preprocessing measurements of electrical impedance tomography to considerably reduce the effect uncertainties in the electrode contacts have on the reconstruction quality, without a need to explicitly estimate the contacts. The idea is to compute the Jacobian matrix of the forward map with respect to the contact strengths and project the electrode measurements and the forward map onto the orthogonal complement of the range of this Jacobian. Using the smoothened complete electrode model as the forward model, it is demonstrated that inverting the resulting projected equation with respect to only the internal conductivity of the examined body results in good quality reconstructions both when resorting to a single step linearization with a smoothness prior and when combining lagged diffusivity iteration with total variation regularization. The quality of the reconstructions is further improved if the range of the employed projection is also orthogonal to that of the Jacobian with respect to the electrode positions. These results hold even if the projections are formed at internal and contact conductivities that significantly differ from the true ones; it is numerically demonstrated that the orthogonal complement of the range of the contact Jacobian is almost independent of the conductivity parameters at which it is evaluated. In particular, our observations introduce a numerical technique for inferring whether a change in the electrode measurements is caused by a change in the internal conductivity or alterations in the electrode contacts, which has potential applications, e.g., in bedside monitoring of stroke patients. The ideas are tested both on simulated data and on real-world water tank measurements with adjustable contact resistances.

math.NA↗