A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient

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Abstract
We compare, through simulations, the performance of four linear algorithms for diffuse optical tomographic reconstruction of the three-dimensional distribution of absorption coefficient within a highly scattering medium using the diffuse photon density wave approximation. The simulation geometry consisted of a coplanar array of sources and detectors at the boundary of a half-space medium. The forward solution matrix is both underdetermined, because we estimate many more absorption coefficient voxels than we have measurements, and ill-conditioned, due to the ill-posedness of the inverse problem. We compare two algebraic techniques, ART and SIRT, and two subspace techniques, the truncated SVD and CG algorithms. We compare three-dimensional reconstructions with two-dimensional reconstructions which assume all inhomogeneities are confined to a known horizontal slab, and we consider two `object-based' error metrics in addition to mean square reconstruction error. We include a comparison using simulated data generated using a different FDFD method with the same inversion algorithms to indicate how our conclusions are affected in a somewhat more realistic scenario. Our results show that the subspace techniques are superior to the algebraic techniques in localization of inhomogeneities and estimation of their amplitude, that two-dimensional reconstructions are sensitive to underestimation of the object depth, and that an error measure based on a location parameter can be a useful complement to mean squared error.