Poster Sessions


変分ベイズ法によるNIRSDOTの逆問題解法とその相転移 演題番号 : P1r21 宮本 敦史 / Atsushi Miyamoto:1 渡辺 一帆 / Kazuho Watanabe:1 池田 和司 / Kazushi Ikeda:1 佐藤 雅昭 / Masaaki Sato:2 1:奈良先端大・情報 / Nara Institute of Science and Technology,Nara, Japan 2:ATR脳情報科学研究所 / Computational Neuroscience Labs, ATR International, Kyoto, Japan Recently, higher cerebral functions have actively been studied because recent noninvasive brain imaging devices enable us to experiment with human subjects. Among them, the near infrared spectroscopy (NIRS) has advantages in safety and ease. A physical model of NIRS is given by the Helmholtz equation, which approximately linearly maps the changes of absorption coefficients to the NIRS data. The NIRSDOT is a method to reconstruct tomographic images from the data by solving the linear equations, which have ambiguity. In a previous study, a solution to the this problem is obtained by the minimumnorm estimation, which assumes that the tomographic images obey Gaussian distributions with homoscedastic variance. However, this gives poor results because it does not take into account the localization of brain activity. The hierarchical Bayes framework is convenient to introduce the localization or sparsity into the model. In fact, it works well in the inverse problem of Magnetoencephalography (MEG) current source estimation.In this study, we apply the hierarchical Bayes framework to the inverse problem of the NIRSDOT. We employ the variational Bayes method to approximate the intractable integration in the framework. Our experiments are taken under two conditions for the NIRSDOT: One is a sparse condition where the change occurs at a point. The other is a nonsparse condition where the changes occur in a spread region.Numerical experiments demonstrate that the hierarchical Bayes framework outperforms the minimumnorm estimation. The framework has the two prior hyperparameters that influence the reconstruction accuracy and sparsity. We observed that the phase transition occurs with respect to the hyperparameters, which causes a sudden change in the sparseness of the tomographic images and the variational free energy that is the objective function of the variational Bayes method. 
