# A Review of Image Reconstruction Algorithms for Diffuse Optical Tomography
## 1 Introduction  
Diffuse optical tomography (DOT) is a biomedical imaging modality that reconstructs the distribution of the optical properties of scattering and absorption coefficients as tomographic images by employing light illumination and detection at the surface of a measured object [1; 2; 3; 4; 5; 6; 7]. Near-infrared (NIR) light propagates deep into tissues and is mainly absorbed by oxy-/deoxyhemoglobin. Therefore, by acquiring DOT with NIR light images, the concentrations of oxy-/deoxyhemoglobin and related oxygen saturation can be determined. This permits diagnosis of diseases such as breast cancer [8; 9; 10; 11; 12] and those involving angiogenesis, and can be used to monitor activities in the human brain [13] and to observe the oxygen supply to the neonatal brain in the intensive care unit [14], both of which are reflected by changes in regional blood flow in the brain. The scattering coefficient can be an indicator of changes in the tissue conditions. Although DOT appears to be a promising novel biomedical imaging technology, it involves technical problems attributed to light propagation accompanied by scattering and absorption. Unlike X-ray computed tomography (CT), image reconstruction employing backprojection does not function well for DOT because of diffusive light propagation. Therefore, DOT requires image reconstruction consisting of two processes. The first is the forward process, which calculates light propagation and predicts measurements. The second is an optimization process that minimizes the error between the actual and predicted measurements. In the forward process, light propagation can be calculated with a given set of absorption and scattering coefficients by employing the radiative transfer equation (RTE) andvarious approximations of the RTE, including the photon diffusion equation (PDE), \(P_{N}\) approximation, and Monte Carlo method. The predicted measurements at the surface of the object are obtained by solving these equations. In the optimization process, a given set of optical properties used in the forward process is updated to minimize the error between the predicted and actual measurements by employing various optimization methods such as the Newton-Raphson method, which minimizes the squared error. The use of regularization techniques and prior information is a good option in the optimization process for some applications. Various image reconstructions can be composed to solve the inverse problem by selecting and combining adequate methods for the forward and optimization processes. Because a strong scattering effect in biological tissues is essentially unavoidable, image reconstruction is crucial for realizing DOT in practical clinical use. Studies on image reconstruction have attempted to resolve the technical problems of spatial resolution and quantification accuracy in DOT images of highly heterogeneous measured objects. Image reconstruction has been improved by the recent studies mentioned in this review, although these efforts have not been reflected in clinical applications. To overcome this low spatial resolution, sparsity regularization techniques related to compressed sensing technology have been introduced. The use of prior information about the structure inside the body obtained from other imaging modalities, such as X-ray CT and magnetic resonance imaging (MRI), has been proposed to improve spatial resolution. Spectral prior information improves the quantification of chromophore concentrations in multispectral DOT imaging. Moreover, changes in the circumstances surrounding DOT in the past two decades affect image reconstruction algorithms. Recent progress in computational technology, including artificial intelligence (AI) and high-performance supercomputers, may have altered image reconstruction of DOT. Image reconstruction schemes employing AI with deep learning in diffuse optical imaging [15; 16; 17; 18; 19] and the simulation of light propagation using supercomputers [20] have also been attempted in recent years.