# A Review of Image Reconstruction Algorithms for Diffuse Optical Tomography
## 4 Optimization Process
### Other Important Topics: Regularization Parameter, Artifacts, Local Minima, and AI
Reconstructions of \(\delta\mu\) and the calibration factors were performed using Tikhonov regularization. \(\delta\mu\) was scaled to be dimensionless for the simultaneous reconstruction. In the numerical experiment with the simulated measurements generated with a randomly chosen calibration factor, no artifacts appeared in the image reconstructed by the proposed method, whereas the images reconstructed without considering the calibration factor were contaminated with artifacts. [PERSON] et al. reported image reconstruction with a calibration factor (coupling coefficient) in FD measurement using a Bayesian framework updating \(\mu_{a}\) and coupling coefficients sequentially [147]. The forward process used the finite difference method. A numerical simulation was performed for a cubic object. The phantom experiments employed a light-emitting diode and a photodiode as the source and detector, respectively. A cylindrical object in a culture flask filled with intralipals was reconstructed. [PERSON] et al. reported the nonlinear reconstruction of \(\mu_{a}\) and \({\mu_{s}}^{\prime}\) and the coupling coefficient to modify the errors in the amplitude and phase in FD measurements [148]. \(\mu_{a}\), \(\mu_{s}\), and the coupling coefficients were scaled by averaging the initial estimates. The FEM was used in the forward process. The damped Gauss-Newton method was used in the optimization process. The 2D numerical simulation and a cylindrical phantom experiment with two targets were performed. In the phantom experiment, hair was placed between the optical fibers and the phantom surface to simulate functional brain imaging. [PERSON] et al. applied a calibration coefficient to TD measurements [149]. The measured amplitude of the DTOF was influenced by changes in the contact condition of the optical fibers on the surface of the measured object, especially when the surface consisted of a soft material such as the skin of the scalp. The mGPST method using the Laplace-transformed DTOF was employed for image reconstruction. In addition to the numerical experiments, a phantom experiment employing a cylindrical polyacetal resin coated with soft silicone rubber demonstrated that the change in compression on the surface by the optical fibers caused an artifact at the surface in the reconstructed image. The calibration coefficient was applied to the in vivo measurement of the infant's head and reduced artifacts. The estimation of the calibration coefficient prior to image reconstruction was proposed by [PERSON] and [PERSON] [150], employing a calibration matrix obtained from a homogeneous phantom, and by [PERSON] et al. [151] using a rotationally symmetric array of source-detector optical fibers in FD measurement. In addition to the instability caused by noise, which is relieved by regularization, the reliability of a reconstructed image is influenced by its nonuniqueness. In particular,using the gradient-based optimization method mentioned in Section 2.3, an initial guess of the optical properties may lead to a local minimum of the cost function, which causes the reconstructed image to not approximate the true image. [PERSON] et al. used a combination of a genetic algorithm (GA) and a gradient-based method in the optimization process to simulate DOT image reconstruction for prostate cancer diagnosis [152]. The GA randomly generated wide-ranging candidates for the reconstructed image, which were updated by mutation, crossover recombination, and selection [153]. The updating rule mimics the biological evolutionary process. The initial guess selected by the GA was used in the nonlinear gradient-based image reconstruction. The FEM geometry, including the prostate, intraprostatic tumor, and rectum, was constructed to solve the PDE based on endorectal MRI images. [PERSON] et al. used simulated annealing (SA) to prevent the reconstructed image from being trapped by local minima [154].