ANN Estimations of the Absorption Coefficient in Multi-Region Heterogenous Media

MoC Solutions as Training Data

Resumo

The estimation of the medium absorption coefficient from external measurements can be stated as an inverse problem [5, 6], and has important applications in optical medicine [8], including in optical tomography [2]. In this work, we propose a framework based on artificial neural networks (ANNs) to estimate the absorption coefficient in multi-region heterogeneous media. The associated direct transport problem [4] is given as a system of equations involving particle intensity I(t, μ, x). The objective is to estimate the absorption coefficient κ(x) from detector measurements d₀(t) = Ψ(t, a) and d₁(t) = Ψ(t, b), t ∈ [0, t_f]. We propose to estimate κ as a piece-wise constant function. The medium is partitioned into n_c cells, which determines the resolution of the estimations. A multi-layer perceptron (MLP) neural network [3] is built to give the κ = (κ_i)_i=1^n_c estimations from discrete detectors measurements d = {(d₀(t_j), d₁(t_j))}_j=1^n_d, where n_d is the number of measurements in discrete times. The ANN is trained from a data set {(d^(s), κ^(s))}_s=1^n_k computed from solutions of the direct problem (1). The direct solver is based on the Method of Characteristics (MoC), and it has already been detailed in our previous work [7]. Therefore, the framework couples an efficient direct solver with a general-purpose non-linear regression model. Further work will include the training of the ANN and the evaluation of the estimations for different resolution setups. The framework is expected to be a powerful alternative for estimating the absorption coefficient in multi-region heterogeneous media. [...]