| The image super-resolution (SR) problem is a generalization of the image restoration problem which is concerned with blur, noise, and aliasing effects. In the context of digital imaging, the purpose of image SR algorithms is to compensate for degradations such as blur resulting from camera motion and inaccurate focusing, sensor noise, and undersampling.;In this thesis, an overview of the most representative SR algorithms is presented. Then, the performance of two state-of-the-art MLSR algorithms based on steepest-descent optimization for grayscale and color images is evaluated and later improved by the introduction of sophisticated quasi-Newton optimization algorithms.;The Davidon-Fletcher-Powell (DFP) and Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithms are appropriately reformulated to cope with the large-scale nature of the SR problem and are then applied to the SR schemes. Experimental results show that by means of the proposed algorithms, grayscale reconstruction is considerably accelerated and the quality achieved in color SR is significantly improved. Moreover, by the introduction of a practical inexact line search, the need for selecting an important parameter is eliminated.;Storage-efficient variants of the BFGS algorithm are also investigated. SR algorithms based on the memoryless BFGS (MBFGS) and limited-memory BFGS (LBFGS) methods are formulated. Experimental results indicate that the proposed algorithms, like the BFGS algorithm, perform the grayscale reconstruction considerably faster and obtain color images of better quality. At the same time, the storage requirements for the MBFGS are comparable to those of the steepest-descent based algorithms while the LBFGS algorithm offers a meaningful trade-off between reconstructed image quality and storage requirements.;Multiframe image SR algorithms can be used to obtain a higher-quality higher-resolution (HR) image by fusing several images that are sub-pixel-shifted versions of the same scene. By means of these algorithms, the task of super-resolving an image is often approached as an inversion problem in which a set of low-quality low-resolution (LR) images is considered to be the result of processing a high-quality high-resolution image through a dynamic image acquisition model. A special class of SR algorithms, known as 'maximum-likelihood super-resolution ' (MLSR) algorithms, utilize a stochastic approach for the inversion of such a model. Basically, the HR image that is most likely to produce the observed LR images is found by solving an optimization problem. |
