arXiv subjects

Pauliina Hirvi

Publications and source records attributed to Pauliina Hirvi.

3 recordsLinked to original sources

arXiv2026

A bilinear inverse problem with forward operator inaccuracy applied to neonatal atlas-based diffuse optical tomography

In this work, we assume to have a set of candidate forward operator matrices and suggest principal component analysis for modeling their variation from the mean. We use this principal component representation to adapt a bilinear inverse-problem formulation to forward-operator inaccuracy in neonatal atlas-based diffuse optical tomography and present two optimization algorithms, as well as Gibbs sampling and a version of the Bayesian approximation error method, for approximately solving the resulting problem. We apply the algorithms to account for the inaccuracy that is present in the sensitivity profiles or Jacobian matrices in diffuse optical tomography when an atlas-based model of the head anatomy is used instead of the subject's own anatomical model in neonates over a wide range of gestational ages (29--44 weeks). We report visual and numerical improvements in the spatial localization and contrast-to-noise-ratio in reconstructions of simulated hemodynamic activity.

math.NA↗

arXiv2026

Computation of frequency- and time-domain Jacobians in optical tomography with Monte Carlo simulations

Significance: Jacobians, or spatially resolved sensitivity profiles, are central to image reconstruction in model-based optical tomography of biological tissue. Although Monte Carlo (MC) simulations are the gold standard for modeling light transport in turbid media, methodology for frequency- and time-domain Jacobians remains incomplete. Aim: This work extends MC to directly compute absorption and scattering Jacobians for frequency-domain (amplitude and phase) and time-domain (intensity and mean time-of-flight) measurements and prism-terminated optical fiber detectors. Approach: Jacobians are derived in the perturbation MC framework and implemented in the high-performance, open-source Monte Carlo eXtreme (MCX) simulator. Results are validated against the diffusion approximation (DA) solved using the finite element method in neonatal head models. MC with split voxels on curved surfaces is extended to Jacobian computation. The detector model is implemented in post-processing and compared with isotropic reception at surface. Results: MC- and DA-derived Jacobians show excellent agreement only in high-scattering regimes, highlighting the importance of MC for low-scattering domains. The detector model reduces surface sensitivity and marginally increases sensitivity to deeper tissues at short (< 2 cm) source-detector separations. Conclusion: A complete theoretical framework and MC software for computing frequency- and time-domain Jacobians is provided. Realistic detector modeling is encouraged for short-separation channels.

physics.comp-ph↗

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↗