Variational Inference With ARD Prior for NIRS Diffuse Optical Tomography

Abstract

Diffuse optical tomography (DOT) reconstructs 3-D tomographic images of brain activities from observations by near-infrared spectroscopy (NIRS) that is formulated as an ill-posed inverse problem. This brief presents a method for NIRS DOT based on a hierarchical Bayesian approach introducing the automatic relevance determination prior and the variational Bayes technique. Although the sparseness of the estimation strongly depends on the hyperparameters, in general, our method has less dependency on the hyperparameters. We confirm through numerical experiments that a schematic phase diagram of sparseness with respect to the hyperparameters has two regions: in one region hyperparameters give sparse solutions and in the other they give dense ones. The experimental results are supported by our theoretical analyses in simple cases.

Comparison of source localization techniques in diffuse optical tomography for fNIRS application using a realistic head model

“…Based on this knowledge, several alternative approaches can be adapted to DOT, such as: minimum norm estimates (MNE) [23], low resolution electromagnetic tomography (LORETA) [24] and Bayesian model averaging (BMA) [25]. To our knowledge, only very few papers have used the Bayesian approach to solve this type of fNIRS inverse problem [26][27][28]. One group has tried a hierarchical Bayesian model for DOT in human brains [26,27] in which different Gaussian priors are used for the blood flow in the scalp (smoother) and the cerebral blood flow.…”

“…One group has tried a hierarchical Bayesian model for DOT in human brains [26,27] in which different Gaussian priors are used for the blood flow in the scalp (smoother) and the cerebral blood flow. Miyamoto et al (2015) proposed the same variational Bayes procedure using the typical prior of automatic relevant determination for the activations, which is similar to minimum norm estimates but using a different hyperparameter to control sparsity of the activation in each voxel [28]. These two methods do not use the BMA approach as this implies evaluating the goodness of different models to solve the inverse problem.…”