| In many applications it is required to reconstruct a single, high resolution image from multiple, degraded low resolution images of the same scene. Additionally, these multiple low resolution images are displaced by sub-pixel shifts with respect to a reference image. Therefore, in order to reconstruct a high resolution image, three sub-problems must be solved. First, the sub-pixel shifts must be found for each frame (the registration step). Second, the noise and the degradation need to be removed from each frame (the restoration step). Finally, the frames need to be interpolated to a uniform grid with a high sampling rate, yielding the desired high resolution image (the interpolation step). Unlike previous work, this thesis takes a more unifying approach, where the three sub-problems are combined into a single step. In order to estimate the displacements, it is essential to combine the registration and restoration steps together. Towards this end, two slightly different approaches are proposed, both of which combine the registration and restoration steps. The difference between the two approaches lies in the interpolation step. In the first approach, called the RR-I formulation, the interpolation step is performed independently of the first two. In the second approach, called the RRI formulation, the interpolation step is combined with the first two steps.; A Maximum Likelihood (ML) formulation has been adopted in solving the above described problem. The log-likelihood function is minimized with the use of the Expectation-Maximization (EM) algorithm. Due to the structure of the matrices, the log-likelihood function is transformed into the frequency domain. In the case of multi-channel image restoration and blur identification, explicit, closed form equations for the parameters of interest can be obtained. In the RR-I approach for high resolution reconstruction, however, closed form equations are no longer possible, although the problem can still be transformed into the frequency domain. Once in the frequency domain, numerical methods are employed to minimize the log-likelihood function. Experimental results are shown which validate both approaches. In addition, the subject of improving the resolution of video is addressed. |
