Three-dimensional non-local edge-preserving regularization for PET transmission reconstruction

Tomographic image reconstruction using statistical methods can provide more accurate system modeling, statistical models, and physical constraints than the conventional filtered backprojection (FBP) method. Because of the ill-posedness of the reconstruction problem, a roughness penalty is often imposed on the solution. To avoid smoothing of edges, which are important image attributes, various edge-preserving regularization schemes have been proposed. Most of these schemes rely on information from a local neighborhood to determine the presence of edges. In this paper, we propose an objective function that incorporates non-local boundary information into the 3-D regularization method. We use an alternating minimization algorithm with deterministic annealing to minimize the proposed objective function to jointly estimate region boundary surfaces and object pixel values. We apply variational techniques implemented using level sets to update the boundary estimates; then, using the most recent boundary information, we minimize a space-variant quadratic objective function to update the image estimate. We present three-dimensional reconstructions from real PET transmission data