For many digital image/video processing applications increasing the spatial resolution is highly beneficial. At higher resolution, TV pictures look more natural and pleasing to the eye, computer vision tasks such as object detection and tracking can be performed with higher precision, medical diagnoses can be made with a higher confidence, security cameras can offer better identification, and satellite imagery can be interpreted with higher accuracy. As such, spatial resolution is an influential parameter in many mainstream imaging applications, and resolution enhancement task naturally arises as a means of increasing the effectiveness of any imaging system used in the mentioned applications. In this thesis, we concentrate on two enhancement problems of practical importance, namely, low-complexity resolution enhancement for customer grade flat panel televisions, and resolution enhancement of noisy high-dimensional hyperspectral imagery. For TV resolution enhancement our main concern is keeping computational complexity at a minimum. The hardware limitations of average customer grade televisions effectively rule out a multi-frame approach. Hence, we take a low-complexity single-frame approach based on exploiting natural image characteristics. For hyperspectral imagery we take advantage of multiple observations in a modified superresolution framework. Here the main challenges are the high dimensionality of hyperspectral data and the noise present in all spectral bands. We design a physical model of the hyperspectral image acquisition process, and based on this model we formulate an iterative resolution enhancement algorithm.