Phase diagrams of a variational Bayesian approach with ARD prior in NIRS-DOT

Diffuse optical tomography is a method used to reconstruct tomographic images from brain activities observed by near-infrared spectroscopy. This is useful for brain-machine interface and is formulated as an ill-posed inverse problem. We apply a hierarchical Bayesian approach, automatic relevance determination (ARD) prior and the variational Bayes method, that can introduce localization into the estimation of the problem. Although ARD enables sparse estimation, it is still open how hyperparameters affect the sparseness and accuracy of the estimation. Through numerical experiments, we present a schematic phase diagram of sparseness with respect to the hyperparameters in the method, which indicates the region of the hyperparameters where sparse estimation is achievable.