In diffuse optical imaging, modulated, near-infrared light is transmitted into the body from an array of detectors placed on the surface of the region to be imaged. The diffuse optical systems then measure the photon fluence that results from the interaction (scattering and absorption) of photons by that region of the body. The goal is to use the diffuse optical data to reconstruct an image of the space varying
optical absorption and reduced scattering coefficients in the region of interest. Because these physical parameters are directly related to the hemodynamic state of tissue, the images can be used to determine, for example, the presence of a tumor in breast tissue.
We present a shape-based approach to 3D image reconstruction from diffuse optical data. We use a low-order parameterization of the background and another for the interior of the anomaly and we use an ellipsoid to describe the boundary of the anomaly. This model has the effect of regularizing the inversion problem and
reducing the dimension of the search space, and it
provides a natural means of modeling other physical properties of the background for additional stability. A damped Gauss-Newton-type
algorithm is implemented to solve the underlying non-linear least squares problem and thereby determine the coefficients of the parameterizations and the descriptors of the ellipsoid. We address some of the underlying computational difficulties and give numerical results illustrating the promise of our approach.
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