Difference imaging aims at recovery of the change in the optical properties of a body based on measurements before and after the change. Conventionally, the image reconstruction is based on using difference of the measurements and a linear approximation of the observation model. One of the main benefits of the linearized difference reconstruction is that the approach has a good tolerance to modeling errors, which cancel out partially in the subtraction of the measurements. However, a drawback of the approach is that the difference images are usually only qualitative in nature and their spatial resolution can be weak because they rely on the global linearization of the nonlinear observation model. To overcome the limitations of the linear approach, we investigate a nonlinear approach for difference imaging where the images of the optical parameters before and after the change are reconstructed simultaneously based on the two datasets. We tested the feasibility of the method with simulations and experimental data from a phantom and studied how the approach tolerates modeling errors like domain truncation, optode coupling errors, and domain shape errors.
The coupled radiative transfer - diffusion model can be used as light transport model in turbid media with non-diffusive regions. In the coupled radiative transfer - diffusion model, light propagation is modelled with the radiative transfer equation in sub-domains in which the approximations of the diffusion equation are not valid and the diffusion approximation is used elsewhere in the domain. In this work, the image reconstruction problem of diffuse optical tomography utilising the coupled radiative transfer - diffusion model is considered. Absorption and scattering distributions are estimated using the coupled radiative transfer - diffusion model as a forward model for light propagation. The results are compared to reconstructions obtained using other light transport models. The results show that the coupled radiative transfer - diffusion model can produce as good estimates for absorption and scattering as the full radiative transfer equation also in situations in which the approximations of the diffusion equation are not valid.
Diffuse optical tomography can image the hemodynamic response to an activation in the human brain by measuring changes in optical absorption of near-infrared light. Since optodes placed on the scalp are used, the measurements are very sensitive to changes in optical attenuation in the scalp, making optical brain activation imaging susceptible to artifacts due to effects of systemic circulation and local circulation of the scalp. We propose to use the Bayesian approximation error approach to reduce these artifacts. The feasibility of the approach is evaluated using simulated brain activations. When a localized cortical activation occurs simultaneously with changes in the scalp blood flow, these changes can mask the cortical activity causing spurious artifacts. We show that the proposed approach is able to recover from these artifacts even when the nominal tissue properties are not well known.
Dental tomographic cone-beam X-ray imaging devices record truncated projections and reconstruct a region of
interest (ROI) inside the head. Image reconstruction from the resulting local tomography data is an ill-posed
inverse problem. A Bayesian multiresolution method is proposed for the local tomography reconstruction. The
inverse problem is formulated in a well-posed statistical form where a prior model of the tissues compensates
for the incomplete projection data. Tissues are represented in a reduced wavelet basis, and prior information
is modeled in terms of a Besov norm penalty. The number of unknowns in the inverse problem is reduced by
abandoning fine-scale wavelets outside the ROI. Compared to traditional voxel based reconstruction methods,
this multiresolution approach allows significant reduction in number of unknown parameters without loss of
reconstruction accuracy inside the ROI, as shown by two dimensional examples using simulated local tomography
A coupled radiative transfer equation and diffusion approximation model for photon migration in tissues is proposed. The light propagation is modeled with the radiative transfer equation in sub-domains in which the assumptions of the diffusion approximation are not valid and the diffusion approximation is used elsewhere in the domain. The coupled equations are solved using the finite element method. The proposed method is tested with simulations. The results of the coupled radiative transfer equation and diffusion approximation model are compared with the finite element solutions of the radiative transfer equation and the diffusion approximation. The results show that the coupled radiative transfer equation and diffusion approximation model can be used to describe photon migration in tissues more accurately than the conventional diffusion model.