A Unified Sparse Recovery and Inference Framework for Functional Diffuse Optical Tomography Using Random Effect Model

Diffuse optical tomography (DOT) is a non-invasive imaging technique to reconstruct optical properties of biological tissues using near-infrared light, and it has been successfully used to measure functional brain activities via changes in cerebral blood volume and cerebral blood oxygenation. However, DOT presents a severely ill-posed inverse problem, so various types of regularization should be incorporated to overcome low spatial resolution and lack of depth sensitivity. Another limitation of the conventional DOT reconstruction methods is that an inference step is separately performed after the reconstruction, so complicated interaction between reconstruction and regularization is difficult to analyze. To overcome these technical difficulties, we propose a unified sparse recovery framework using a random effect model whose termination criterion is determined by the statistical inference. Both numerical and experimental results confirm that the proposed method outperforms the conventional approaches.