  Diffuse optical tomography (DOT) utilises near-infrared light for imaging
spatially distributed optical parameters, typically the absorption and
scattering coefficients. The image reconstruction problem of DOT is an
ill-posed inverse problem, due to the non-linear light propagation in tissues
and limited boundary measurements. The ill-posedness means that the image
reconstruction is sensitive to measurement and modelling errors. The Bayesian
approach for the inverse problem of DOT offers the possibility of incorporating
prior information about the unknowns, rendering the problem less ill-posed. It
also allows marginalisation of modelling errors utilising the so-called
Bayesian approximation error method. A more recent trend in image
reconstruction techniques is the use of deep learning techniques, which have
shown promising results in various applications from image processing to
tomographic reconstructions. In this work, we study the non-linear DOT inverse
problem of estimating the absorption and scattering coefficients utilising a
`model-based' learning approach, essentially intertwining learned components
with the model equations of DOT. The proposed approach was validated with 2D
simulations and 3D experimental data. We demonstrated improved absorption and
scattering estimates for targets with a mix of smooth and sharp image features,
implying that the proposed approach could learn image features that are
difficult to model using standard Gaussian priors. Furthermore, it was shown
that the approach can be utilised in compensating for modelling errors due to
coarse discretisation enabling computationally efficient solutions. Overall,
the approach provided improved computation times compared to a standard
Gauss-Newton iteration.
