Information loss and reconstruction in diffuse fluorescence tomography

This paper is a theoretical exploration of spatial resolution in diffuse fluorescence tomography. It is demonstrated that, given a fixed imaging geometry, one cannot-relative to standard techniques such as Tikhonov regularization and truncated singular value decomposition-improve the spatial resolution of the optical reconstructions via increasing the node density of the mesh considered for modeling light transport. Using techniques from linear algebra, it is shown that, as one increases the number of nodes beyond the number of measurements, information is lost by the forward model. It is demonstrated that this information cannot be recovered using various common reconstruction techniques. Evidence is provided showing that this phenomenon is related to the smoothing properties of the elliptic forward model that is used in the diffusion approximation to light transport in tissue. This argues for reconstruction techniques that are sensitive to boundaries, such as L1-reconstruction and the use of priors, as well as the natural approach of building a measurement geometry that reflects the desired image resolution.