Deep Learning of Diffuse Optical Tomography Based on Time-Domain Radiative Transfer Equation

Near infrared diffuse optical tomography (DOT) is a potential tool for diagnosing cancer by image reconstruction of tissue optical properties. A variety of image reconstruction methods for DOT have been attempted, in general, based on the diffusion equation (DE). However, the image quality is still insufficient to clinical use, which is mainly attributed to the fact that the DE is invalid in some regions, such as low-scattering regions, and the inverse problem is inherently ill-posed. In contrast, the radiative transfer equation (RTE) accurately describes light propagation in biological tissue and also the DOT by deep learning is recently thought to be an alternative approach to the inverse problem. Distribution of time of flight (DTOF) of photons estimated by the time-domain RTE lends itself to deep learning along a temporal sequence. In this study, we propose a new DOT image reconstruction algorithm based on a long-short-term memory and the time-domain RTE. In simulation studies, using this algorithm, we succeeded in detection of an absorbing inclusion with a diameter of 5 mm, an absorber mimicking cancer, which was embedded in a two-dimensional square model (4 cm x 4 cm) with an optically homogeneous background. Multiple absorbers and a bigger absorber embedded in this model were also detected. We also demonstrate that, if simulation data by beam injection from multiple directions are employed as a training set, the accuracy of detection is improved especially for multiple absorbers.