Regularized Image Up-sampling

This thesis addresses the problem of performing image magnification to achieve higher perceived resolution for grey-scale and color images. A new perspective on the problem is introduced through the new concept of a theoretical camera that can acquire an ideal high resolution image. A new formulation of the problem is then introduced using two ingredients: a newly designed observation model and the total-variation regularizer. An observation model, that establishes a generalized relation between the desired magnified image and the measured lower resolution image, has been newly designed based on careful study of the physical acquisition processes that have generated the images. The result is a major contribution of this thesis: a closed-form solution for obtaining the observation model. This closed form has been implemented and observation models were obtained for different typical scenarios, and their performance was shown to outperform observation models used in the literature. Two new theorems for designing the theoretical camera, adapted to the display device used, on arbitrary lattices have been developed. The thesis presents new analysis with a signal processing perspective that justifies the use of the total-variation regularizer as a priori knowledge for the magnified image; this analysis is defined on both the low and the high resolution lattices simultaneously. The resulting objective function has been minimized numerically using the level-set method with two new motions that interact simultaneously, leading to a solution scheme that is not trapped in constant-image solutions and converges to a unique solution regardless of the initial estimate. For color images, the human visual system characteristics were involved in the choice of the color space used in the implementation. It was found that a proper color space such as YCbCr that focuses on magnifying a better luminance channel provided the same result as a vectorial total-variation formulation, but at a reduced computational cost. The quality of the magnified images obtained by the new approaches of this thesis surpassed the quality of state-of-the-art methods from the literature.