Time-Varying Image Restoration Using Extended Kalman Filter

In this paper, the original clean magnetic resonance (MR) image is restored by taking noisy measurements on the image field. The restoration of MR image is carried out by modeling a dynamically varying image field driven by white Gaussian noise (WGN) using a linear partial differential equation (pde). The pde is considered to be of the first order in time and arbitrary order in the two spatial coordinates. But, the measurement data is available only on a few pixels rather than on the entire image field. So, the formulation of image dynamic model accounts for the remaining information about the image required for the purpose of restoring the original clean image. Finally, Extended Kalman Filter (EKF) is applied to dynamically estimate the parameters of the pde from the sparse measurement of the noisy image field. Simulation results are presented to exhibit the quality of reconstructed MR images from the proposed EKF technique.