Multi-frame Super-Resolution (SR) techniques obtain a high resolution (HR) image by fusing multiple low-resolution (LR) observations. The image acquisition process of SR is modeled as an original HR image being warped, blurred, down-sampled and added with noise to generate LR images. Motion (presented as warping) produces multiple observations of the same scene, attaining the sampling diversity which is the key to SR. While the translational warping is easy to handle, non-translational warping is more difficult because when registering all LR images to a HR grid, the sample pattern is non-periodic. Existing methods for SR with non-translational warping are either troubled by artifacts or very slow. We present a regularized SR reconstruction method to solve the SR problem under non-translational motion. The warping is implemented as an image operator, the same as blurring and down-sampling operators. All the operators are incorporated in one cost function and are implemented efficiently using fast parallel methods, without creating large matrices. Experimental results show the effectiveness of the proposed method. In this part of dissertation, the blurring function is assumed to be known, however this method is the foundation of the following part, the blind SR under non-translational motion.;The next part of the dissertation presents a blind SR framework that can estimate the image and the blurring point spread function (PSF) simultaneously. In such a framework, the alternating minimization (AM) scheme is adopted, where the PSF and image are estimated in an alternating way. The blind estimation may result in a trivial solution (PSF is delta and HR image is blurry). To push the iteration toward the true solutions, an L0 gradient minimization is implemented on the current estimated HR image in each iteration. The L0 gradient minimized image contains only salient edges and can mimic the unknown sharp image for PSF estimation. When estimating the PSF, the original cost function needs manipulations to make the PSF explicit. It is straightforward for translation case, but very difficult for non-translational motion model, because the warping and the blur are not commutable anymore. To tackle this problem, the warped image is used directly and the warping is not considered as a separate operator, which avoids the non-commutable issue in PSF estimation. Another advantage of this approach is its ability to handle the variable PSF-problem, which is common when the image acquisition conditions are different among the LR images, for example the video frames with occasional motion blur or the images captured by different cameras. Experimental results suggest the effectiveness of the proposed method in all scenarios.;Based on L0 gradient minimization and different observation model selections for image and PSF estimation, we introduce a blind estimation framework that solves the challenging blind SR under non-translational motion problem. The promising experimental results suggest that the proposed method outperforms state-of-the-art methods in both fix-PSF and variable-PSF conditions.
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