# A Review of Image Reconstruction Algorithms for Diffuse Optical Tomography
## 4 Optimization Process
### Use of Structural Prior Information  
Because DOT provides functional information, the interpretation of DOT images becomes more meaningful by superimposing DOT images onto morphological images obtained by other imaging modalities, such as X-ray CT, MRI, and ultrasound imaging. Moreover, information regarding the location where the optical properties can change improves the precision and efficiency of image reconstruction by reducing the number of unknown variables to be reconstructed. [PERSON] and [PERSON] proposed a two-stage image reconstruction method that employs prior information [120]. They assumed that the anatomical structure inside a measured object can be obtained using other imaging modalities. The averages of the optical properties in certain regions obtained by the segmentation of other images were reconstructed in the first stage. In the first stage, the optical properties of each region were assumed to be homogeneous. Subsequently, the details of the optical properties in each region were reconstructed in the second stage by employing the image obtained in the first stage as an initial estimate. It was demonstrated that the proposed two-stage method employing a segmented MR image of the brain provides a better image than image reconstruction with a homogeneous flat initial estimate. [PERSON] et al. incorporated prior information into the matrix \(J\)[121]. The discretized positions (FEM node) in a segmented region were lumped by introducing a \(K\times K\) matrix \(U\) that had elements \(U_{\xi,\eta}=1\) when the \(\xi\)-th position was included in \(\eta\)-th segmented region, and was otherwise 0. The matrix \(J\) in Equation (9) was replaced by the matrix \(JU\). The ill-posed nature of the inverse problem was relieved by grouping the discretizedpositions. The accuracy of the reconstructed values improved significantly in the 3D image reconstruction of small objects. The prior information that was introduced into \(U\) to fix a homogeneous change in the optical properties in a segmented region is called the hard prior information. [PERSON] et al. employed a hard prior method to quantify hemoglobin concentration and oxygen saturation of breast lesions in 14 subjects [122]. They obtained prior structural information from the MR images. Image reconstructions of \(\mu_{a}\) at wavelengths of 780 and 830 nm were carried out for the regions of the tumor and other tissues (background). The cancerous tumor had a hemoglobin concentration almost 10 times higher than that of the background tissues and the oxygen saturation of cancerous tissues was approximately 10% lower than that of the background tissues. [PERSON] et al. investigated the influence of imperfect prior information, which are errors in the segmentation of MIR images, on two-step image reconstruction combined with background estimation with nonlinear optimization and linearized image reconstruction with a hard prior method [123]. By comparing the image reconstructed from the homogeneous initial guess with that from the initial guess obtained based on prior background information, it was demonstrated that image reconstruction with imperfect prior information can localize the abnormal region in the breast but causes a bias in the reconstructed image. [PERSON] et al. tried using hard prior information from ultrasound images in TD measurements with eight wavelengths ranging from 635 to 1060 nm [124]. Digital phantoms of the breast were used to visualize benign and malignant lesions. The digital phantoms were generated using software from the Virtual Imaging Clinical Trials for Regulatory Evaluation (VICTRE) Project. B-mode ultrasound images of the breast were simulated using \(k\)-wave software [125] by employing phantoms. The optical properties were determined using Gaussian random variables, which had different averages and variances between the benign and malignant lesions. For image reconstruction, segmentations were performed to separate the lesion and normal regions based on the B-mode image.