In recent years, the substantial increase in the number of spectral channels in optical remote sensing sensors allows more detailed spectroscopic analysis of objects on the Earth surface. Modern hyperspectral sensors are able to sample the sunlight reflected from a target on the ground with hundreds of adjacent narrow spectral channels. However, the increased spectral resolution comes at the price of a lower spatial resolution, e.g. the forthcoming German hyperspectral sensor Environmental Mapping and Analysis Program (EnMAP) which will have 244 spectral channels and a pixel size on ground as large as 30 m x 30 m. The main aim of this thesis is dealing with the problem of reduced spatial resolution in hyperspectral sensors. This is addressed first as an unmixing problem, i.e., extraction and quantification of the spectra of pure materials mixed in a single pixel, and second as a resolution enhancement problem based on fusion of multispectral and hyperspectral imagery. This thesis proposes novel methods for hyperspectral unmixing using sparse approximation techniques and external spectral dictionaries, which unlike traditional least squares-based methods, do not require pure material spectrum selection step and are thus able to simultaneously estimate the underlying active materials along with their respective abundances. However, in previous works it has been shown that these methods suffer from some drawbacks, mainly from the intra dictionary coherence. To improve the performance of sparse spectral unmixing, the use of derivative transformation and a novel two step group unmixing algorithm are proposed. Additionally, the spatial homogeneity of abundance vectors by introducing a multi-look model for spectral unmixing is exploited. Based on the above findings, a new method for fusion of hyperspectral images with higher spatial resolution multispectral images is proposed. The algorithm exploits the spectral information of the hyperspectral image and the spatial information from the multispectral image by means of sparse spectral unmixing to form a new high spatial and spectral resolution hyperspectral image. The introduced method is robust when applied to highly mixed scenarios as it relies on external spectral dictionaries. Both the proposed sparse spectral unmixing algorithms as well as the resolution enhancement approach are evaluated quantitatively and qualitatively. Algorithms developed in this thesis are significantly faster and yield better or similar results to state-of-the-art methods.