Estimation-theoretic algorithms and bounds for three-dimensional polar shape-based imaging in diffuse optical tomography

In the case where we have prior knowledge that a medium can be well approximated as being piecewise constant, we can resolve edges in three-dimensional diffuse optical tomography, generally thought of as a low-resolution imaging modality due to the extremely smoothing nature of the diffusion operator. Assuming that the piecewise-constant regions are polar, we parametrize the boundary using spherical harmonics, reducing the inverse problem to a low-dimensional parameter estimation problem. We show how the sensitivity of the forward model to shape variations can be efficiently, directly computed. The resulting shape Jacobian is used both in the context of an estimation algorithm for determining these parameters and as the basis for Cramer-Rao bounds calculations that provide for an understanding of the fundamental limits on our ability to resolve shape structure from DOT data