A Model-Based Iterative Learning Approach for Diffuse Optical Tomography

Abstract

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 socalled Bayesian approximation error method. A more recent trend in image reconstruction techniques is the use of deep learning , which has 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 (absolute) 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.

Sequential model correction for nonlinear inverse problems

“…Finally, we will consider the application of the sequential approximation for the use with other nonlinear PDE based inverse problems [22,29]. Here, we believe that the fixed approximation without the need to compute the Jacobian could be of great computational advantage.…”

“…Naturally, AEM has trouble dealing with non-Gaussian approximation errors, which we also illustrate. To overcome this limitation, some recent works have proposed neural networks for model correction [12,16,20,22,33], in which case the correction is nonlinear. Neural networks succeed in the task but require training data that represent the solution space well enough.…”

DeepEIT: Deep Image Prior Enabled Electrical Impedance Tomography

“…The proposed method discussed here is, however, not limited to EIT. The proposed framework handles the task of recovering images and may consequentially be used for other applications requiring image reconstruction, e.g., diffuse optical tomography [13] and electrical capacitance tomography [14].…”

Machine Learning Diffuse Optical Tomography Using Extreme Gradient Boosting and Genetic Programming

“…Yoo et al [ 15 ] developed a novel DL algorithm that accurately detects anomalies in beast tissues by inverting the Lippman–Schwinger equation, achieving significant results. In a more recent study, Mozumder et al [ 29 ] employed a model-based DL approach to improve the estimation of the absorption and scattering coefficient of diffuse media. It was shown in this study that the proposed DL method also significantly reduces computation time.…”