A Modular Deep Learning-based Approach for Diffuse Optical Tomography Reconstruction

TL;DR

This paper tackles the ill-posed inverse problem of Diffuse Optical Tomography (DOT) by introducing Mod-DOT, a modular deep learning framework that separates data and signal representations via autoencoders and links their latent spaces with a bridge network acting as a learned regularizer. The approach leverages decoupled pretraining, a denoising component, and convolutional architectures to reconstruct the absorption coefficient field from boundary measurements more robustly than traditional variational methods or end-to-end networks. Extensive synthetic experiments show Mod-DOT markedly improves recovery under realistic noise levels, with convolutional variants delivering better performance and pretraining enhancing stability. The results suggest substantial practical potential for fast, regularized DOT reconstructions in clinical-like settings, while situating Mod-DOT within the broader context of learned regularization and reduced-order modeling for inverse problems.

Abstract

Medical imaging is nowadays a pillar in diagnostics and therapeutic follow-up. Current research tries to integrate established - but ionizing - tomographic techniques with technologies offering reduced radiation exposure. Diffuse Optical Tomography (DOT) uses non-ionizing light in the Near-Infrared (NIR) window to reconstruct optical coefficients in living beings, providing functional indications about the composition of the investigated organ/tissue. Due to predominant light scattering at NIR wavelengths, DOT reconstruction is, however, a severely ill-conditioned inverse problem. Conventional reconstruction approaches show severe weaknesses when dealing also with mildly complex cases and/or are computationally very intensive. In this work we explore deep learning techniques for DOT inversion. Namely, we propose a fully data-driven approach based on a modularity concept: first data and originating signal are separately processed via autoencoders, then the corresponding low-dimensional latent spaces are connected via a bridging network which acts at the same time as a learned regularizer.

Figures (14)

• Figure 1: Biological tissues are complex structures belonging to the class of turbid media with respect to light propagation. An incident light beam may undergo reflection, refraction, absorption and scattering. Of the penetrating photons, only a limited number of emerge from the sample via unscattered transmission, the most part of them being instead subjected to multi-scattering events.
• Figure 2: Scattering in biological tissues causes a ray of light coming from direction ${{\bm s}}$ to be scattered by a particle in position ${\bm r}$ in direction ${{\bm s}}^{\, \prime}$ around a cone of angle $d{{\bm s}}^{\, \prime}$.
• Figure 3: Workflow in the Mod-DOT approach. Observed data and originating signal are encoded individually in the corresponding latent spaces via the data-AE and the signal-AE, respectively (violet arrow paths). Latent spaces are then connected via the bridge-NN. At test time, the reconstruction process consists in the cascade application of the three networks (red arrow path) $\mathcal{N}:= \mathcal{D}_\mu \circ \Sigma \circ \mathcal{E}_y$.
• Figure 5: Workflow in the DL-ROM approach (here shown for comparison with the present approach). First, the AE $\mathcal{D}_\phi \circ \mathcal{E}_\phi$ is trained to learn an approximation of the identity operator over the solution manifold (violet arrow) using FOM snapshots obtained by a computationally intensive computation. This AE provides the latent low--dimensional representation ${\bm z}_\phi$ of the solution manifold. Then, the network $\Sigma_\phi$ is trained to learn the map ${\bm q}^h \rightarrow {\bm z}_\phi$ (dark yellow arrow). Finally, the composition $\mathcal{D}_\phi \circ \Sigma_\phi$ defines the DL-ROM approximation of the parameter-to-state map at test time (red arrow).
• Figure 6: Geometry of the semi-disk and rectangular domains considered in the numerical experiments. The detectors are uniformly disposed along the curved boundary for the semi-disk and top/left/right boundary for the rectangle domain; the sources are aligned along the bottom boundary and positioned 1mm inside the domain. The absorption coefficient is $\mu_{a,0}$ except for the contrast regions (circular areas) which have increased absorption coefficient.

Theorems & Definitions (1)

• Remark 1