# A Review of Image Reconstruction Algorithms for Diffuse Optical Tomography
## 4 Optimization Process
### Use of Structural Prior Information
Two-region image reconstruction was performed, and the reconstructed optical properties were used for classification, in which 75% of the lesions were classified correctly. In contrast, the prior information incorporated into the regularization term was called soft prior information [25]. In this approach, prior information was incorporated into matrix \(L\) in Equation (9). One of the methods for employing \(L\) as prior information is to use the elements of \(L_{k,k^{\prime}}=1\) when \(k=k^{\prime}\), \(L_{k,k^{\prime}}=0\) when \(k\
eq k^{\prime}\), and \(L_{k,k^{\prime}}=-1/K\) when the \(k\)-th and \(k^{\prime}\)-th FEM nodes are in the same segmented region (Laplacian structure). Using this method, the difference in optical properties at positions in the same segmented region was minimized. Therefore, the optical properties tended to be homogeneous in each segmented region. [PERSON] et al. examined soft and hard prior methods [126; 127] in numerical simulations with an MRI-based breast model and an experiment with a gelatin phantom. The Laplacian and Helmholtz structures were used as soft prior methods. In the Helmholtz structure, which is a modified version of the Laplacian structure, \(L_{k,k^{\prime}}=-1/(K+h/l)\) when the \(k\)-th and \(k^{\prime}\)-th FEM nodes are used in the same segmented region, where \(h\) and \(l\) are the distances between the nodes and the size of the imaging target (tumor), respectively. Compared with image reconstruction without prior information, the use of structural prior information dramatically improves the quantification and image quality of DOT. [PERSON] et al. used the soft prior method with MR to reconstruct the optical properties of the breast using FD measurements [128]. In numerical simulations, the soft prior method with a tissue layer structure recovered 74% of the true values. Additionally, a good initial estimate of the optical properties provided 99% recovery. [PERSON] et al. proposed a method that uses prior information on the structure obtained using other imaging modalities in the regularization term [129]. Using the diagonal matrix \(L\), which has a diagonal element of 1 corresponding to the voxel in the segmented tumor region and 0 corresponding to the normal region, the cost function with the regularization terms was formulated with linearization in the forward process as  
\[\|\delta\mathbf{M}-J\delta\mathbf{\mu}\|^{2}+\gamma_{1}\|(I-L)\delta\mathbf{\mu} \|^{2}+\gamma_{2}\|L\delta\mathbf{\mu}\|^{2}. \tag{24}\]  
By taking a large value of the regularization parameter \(\gamma_{1}\) and a small value of \(\gamma_{2}\), \(\delta\mu\) in the tumor region can become relatively large, although the artifacts, which are noises that appear in the reconstructed image, can be enhanced. In this study, the spectral prior method described in Section 4.3 was also employed. The Bayesian framework incorporates prior structural information. [PERSON] et al. proposed a hierarchical Bayesian approach [130]. Anatomical images, such as MRI and X-ray CT, were segmented into subimages composed of background tissues. In each subimage, we assumed that the absorption coefficient was Gaussian distributed with an unknown mean and variance, which are referred to as the hyperparameters. The FD measurements were then modeled with linearization employing the Rytov approximation and additive Gaussian noise. The hierarchical Bayesian approach estimated \(\delta\mu_{a}\) and the hyperparameters simultaneously by maximizing the log-likelihood of the posterior probability density function. In a manner different from the Bayesian framework, [PERSON] et al. treated DOT image reconstruction with probability statistics to incorporate prior structural information [131]. For the regularization term, they used the joint entropy and mutual information of the reconstructed and reference images obtained by different imaging modalities.