Joint estimation of offset parameters and high-resolution images via l1-norm minimization principle

We propose a joint estimation algorithm of offset parameters and a high resolution image from a set of multiple low resolution images based on the l₁-norm minimization principle. Advantages of the joint approach include that, since it uses low-resolution images in a batch manner, we are less suffered from aliasing effects. The l₁-norm minimization principle is effective because we assume sparsity on underlying high-resolution images. The proposed algorithm first minimizes the l₁-norm of a vector that satisfies data constraint with the offset parameters fixed. Then, the minimum value is further minimized with respect to the parameters. Even though this is a heuristic approach, the computer simulations show that the proposed algorithm perfectly reconstructs sparse images with a probability more than or equal to 99% for large dimensional images. The proposed approach is attractive because of its computational efficiency.