State space regularization in the nonstationary inverse problem for diffuse optical tomography

Abstract

In this paper, we present a regularization method in the nonstationary inverse problem for diffuse optical tomography (DOT). The regularization is based on a choosing time evolution process such that in a stationary state it has a covariance function which corresponds to a process with similar smoothness properties as the first-order smoothness Tikhonov regularization. The proposed method is computationally more lightweight than the method where the regularization is augmented as a measurement. The method was tested in the case of the inverse problem of DOT. A solid phantom with optical properties similar to tissue was made, incorporating two moving parts that simulate two different physiological processes: a localized change in absorption and a surrounding rotating two-part shell which simulates slow oscillations in the tissue background physiology. A sequence of measurements of the phantom was made and the reconstruction of the image sequence was computed using this method. It allows the recovery of the full time series of images from relatively slow measurements with one source active at a time. In practice, this allows instruments with a larger dynamic range to be applied to the imaging of functional phenomena using DOT.