# Deep Learning of Diffuse Optical Tomography Based on Time-Domain Radiative Transfer Equation  
[PERSON]  
1 Center for Computational Sciences, University of Tsukuba, 1-1-1 Tennoudai, Tsukuba 305-8  
The propagation of light in turbid media with absorption is governed by the radiative transfer equation (RTE) [2]. Numerical schemes to directly solve the RTE in biological tissue have been proposed [3; 4]. However, they are computationally expensive, since RTE in three-dimensional space results in a six-dimensional problem in photon phase space. In addition, for the solution of the inverse problem to converge, the forward problem must be solved multiple times for a single reconstruction. Therefore, the RTE calculations have been a bottleneck in algorithms when solving the inverse problem. Thus far, light propagation has often been approximated by a diffusion equation (DE) using the P1 approximation of the RTE. The diffusion approximation is a simplification of the RTE for optically thick media in which multiple scattering is dominant [5]. Based on frequency-domain as well as time-domain DE, various approaches for image reconstruction in DOT have been attempted [6].  
However, actual tissue systems are in the so-called mesoscopic scattering regime, in which light undergoes multiple scattering but the scattered light is not perfectly diffusive. For mesoscopic scattering, the diffusion approximation breaks down especially near sources and boundaries. To circumvent the shortcomings of the diffusion approximation, hybrid schemes that combine radiative transfer with diffusion have been implemented [7; 8]. Hybrid schemes can reduce the computational cost to solve light propagation dramatically, but the transition between RTE and DE cannot be determined a priori. Therefore, full RTE calculations are desirable. As for the frequency-domain RTE, several solvers of the inverse problem have been proposed [9; 10]. Since, however, image reconstruction based on time-domain RTE is still immature, we have recently developed a time-domain RTE solver, TRINITY (Time-dependent Radiation Transfer in Near-infrared Tomography) [11], which is based on our former steady-state RTE solver, ART [12].  
Deep learning brings a new possibility for image reconstructions. Thus far, most deep learning schemes for DOT have been based on DE [13; 14; 15], although a deep learning scheme based on the steady RTE has also been developed [16]. However, no attempt has yet been made for the time-domain RTE. In this study, we construct a novel DOT algorithm based on deep learning and a time-domain RTE, in which DTOFs are used as training data. As for the deep learning, we utilize an LSTM (Long Short-Term Memory) method, which is an extension of the artificial recurrent neural network (RNN) architecture to process not only single data points but entire sequences of temporal data. We apply this algorithm to detect highly absorbing areas in a two-dimensional mathematical model of biological tissue with the optically homogeneous background. The approach similar to ours has been reported by the other research group, whereas this study employed an FD DOT system [15].  
In this paper, firstly we describe the details of the algorithm and image reconstruction of a single absorber with datasets obtained from a single beam injection. Then, we present image reconstruction of multiple absorbers with a subtraction method and improvement of image quality by using datasets obtained from multiple beam injections.