Optimal interpolation for medical images using MAP method

The problems of high resolution image reconstruction are approached in this project as an optimization problem. Assuming an ideal image is blurred, noise corrupted, and sub-sampled to produce the measured image, we pose the estimation of the enlarged image as a maximum-a-posteriori (MAP) restoration process and the mean field annealing optimization technique is used to solve the multi-model objective function. The iterative interpolation process incorporates two terms into its objective function. The first term is the 'noise' term which models the burring and subsampling of the acquisition system. By using the system point spread function and the noise characteristics, the measured pixels at the sub-sampled-grid are mapped into the grid of the original image. A second term, the a-priori term is formulated to fore the prior constraints such as noise smoothing and edge preserving into the interpolation process. The resulted image is a noise reduced, deblurred, and enlarged image. The proposed algorithm are used to zoom several medical images, along with existing techniques such as pixel replication, linear interpolation, and spectrum extrapolation. The resulted images indicate that the proposed algorithm can smooth noise extensively while keeping the image features. The images zoomed by other methods suffer from noise and look less favorable in comparison.