DOT for Molecular Imaging
The optical properties of a highly scattering medium such as tissue can be reconstructed noninvasively by diffuse optical tomography (DOT) based on measurements of scattered and attenuated optical flux. However, due to the diffusive nature of light propagation, the inverse problem of DOT is severely ill-posed and nonlinear. Even though linearized approach or iterative methods that update Green's function are widely used to reconstruct optical parameters, these approaches suffer from the approximation error or the computational burden of the iterative procedures. Recently, we found that DOT problems in practice can be understood in the framework of the compressed sensing, based on the sparse nature of the perturbation in optical properties and showed that the original DOT inverse problem can be changed to the joint sparse recovery problem. The joint sparse recovery tep gives us unknown fluence on the estimated support set, which eliminates the non-linearity in an integral equation for the simultaneous estimation of the optical parameters.
The non-linearity of the DOT inverse problem had been an unsolved problem for a long time. We proposed a method based on compressed sensing theory, especially joint sparsity, to resolve it and showed improved reconstruction results with less computational complexity compared to conventional methods. We also found that the proposed method is less prone to cross-talk phenomenon under CW mode. The proposed method can be used in not only DOT problem but also electric impedance tomography (EIT), microwave imaging, etc, related to the non-linear inverse problem.
DOT for Functional Brain Imaging
One of the applications of DOT problem is the functional brain imaging. In this problem, we exploited multiple measurements from near-infrared spectroscopy equipment and the assumption of the spatial sparsity of the neural activation. Therefore, joint sparsity was considered as the temporal variations of oxy- and deoxy-hemoglobin concentration in sparse activation area, and the conventional functional DOT problem was converted into the joint sparse recovery problem. Here, we applied array signal processing approach, especially MUSIC (MUltiple SIgnal Classification) algorithm, using an abundant temporal measurements from the NIRS equipment. We also applied the false discovery rate (FDR) to control the family-wise error rate of the statistical map based on the assumption that the resultant MUSIC spectrum follows the chi-squared distribution. Various simulation studies and right finger tapping experiment showed the validity of the proposed method, and comparison with that of the fMRI showed it's potential practicality.
The proposed method takes full advantage of the abundant temporal information from the NIRS equipment to connect the conventional functional brain imaging problem of DOT to the field of array signal processing. The additional benefit from that is it works even when the experimental paradigm is not known, whereas it is essential to apply general linear model (GLM) approach.