The objective of the proposed research is to develop high performance, low computational complexity resolution enhancement and demosaicing algorithms. Our approach to both problems is to find creative ways to incorporate edge information into the algorithm design. However, in contrast with the usual edge directed approaches, we do not try to detect edge presence and orientation explicitly. For the image interpolation problem, we study the relationship between low resolution and high resolution pixels, and derive a general interpolation formula to be used on all pixels. This simple interpolation algorithm is able to generate sharp edges in any orientation. We also propose a simple 3 by 3 filter that quantifies local luminance transition and apply it to the demosaicing problem. Additionally, we propose a gradient based directional demosaicing method that does not require setting any thresholds. We show that the performance of this algorithm can be improved by using multiscale gradients. Finally, we address the low spectral correlation demosaicing problem by proposing a new family of hybrid color filter array (CFA) patterns and a local algorithm that is two orders of magnitude faster than a comparable non-local solution while offering the same level of performance.