Tumor detection using Bayesian conjugate prior in diffuse optical tomography

Diffuse optical tomography (DOT) is an emerging non-invasive technique for detecting the presence of a tumor or other anomalies from a scattered photon field. In this paper, we derive an alternating projection algorithm to reconstruct the spatially varying absorption coefficient of human brain tissue to detect the presence of tumor. We use a perturbation method and assume the absorption coefficient of the tumor to be spatially varying with a Gaussian distribution. This assumption serves as a Bayesian conjugate prior on the absorption coefficient of the whole domain and using this prior can reduce the computational complexity and allow finding analytically tractable posteriors. Such prior information can be extracted from MRI or X-ray images to improve spatial resolution and accuracy of the reconstructed image. We illustrate our results using a simulated 3D geometry. We show that tumor presence can be detected using only one observation of the noisy data.