Robust fusion of MRI and ECT data, and acceleration of EM algorithm using proximal point approach

A robust multisensor fusion approach to use prior information from one sensor data to regularize an inverse problem based on another sensor data is presented. The robust approach is based on minimax rules. We apply this method to an application in medical imaging where anatomical boundary information from Magnetic Resonance Imaging (MRI) or X-ray Computed Tomography data is used to improve Emission Computed Tomography (ECT) image reconstruction.;A parametric model is used to extract boundary information from MRI image. We derive asymptotic expressions for Cramer-Rao (CR) bound for extraction for 2-D and 3-D shapes and present shapes that are estimated with least uncertainty and most uncertainty. We also discuss how to find the optimum center to extract the shape with least uncertainty.;We derive an asymptotic expression for the minimax objective to get a penalized likelihood objective with quadratic penalty. The penalty weights are smoothed proportional to the uncertainty in boundary estimate. We implement a method that approximates this asymptotic approach to combine 2-D MRI and ECT data. Robustness of estimate of radioactive tracer uptake in a simple region of interest is achieved using this method.;Finally, we apply proximal point approach to accelerate the Expectation Maximization (EM) algorithm. The EM algorithm is used to maximize likelihood and has linear convergence rate. Hence acceleration of EM algorithm is essential. The method is applied for two separate problems namely, reconstruction of 1-D signal and 2-D image from their noisy projections.