Theory and Implementation of Minimax Ect Image Reconstruction with Mri Side Information

In this report a minimax methodology is presented for combining information from two imaging modalities having diierent intrinsic spatial resolutions. The focus application is emission computed tomography (ECT), a low resolution modality for reconstruction of radionuclide tracer density, when supplemented by high resolution anatomical boundary information extracted from a magnetic resonance image (MRI) of the same imaging volume. The MRI boundary within the 2D slice of interest is parameterized by a closed planar curve. The Cram er-Rao (CR) lower bound is used to analyze estimation errors for diierent boundary shapes. Under a spatially inhomogeneous Gibbs eld model for the tracer density a representation for the minimax MRI-enhanced tracer density estimator is obtained. It is shown that the estimator is asymptotically equivalent to a penalized maximum likelihood (PML) estimator with resolution-selective Gibbs penalty. Quantitative comparisons are presented using the iterative Space Alternating Generalized Expectation Maximization (SAGE-EM) algorithm to implement the PML estimator with and without minimax weight averaging.