In this dissertation, I design a processing approach, implement and test several solutions to combining spatial and spectral processing of multisource data. The measured spectral information is assumed to come from a multispectral or hyperspectral imaging system with low spatial resolution. Thematic content from a higher spatial resolution sensor is used to spatially localize different materials by their spectral signature. This approach results in both spectralunmixing and sharpening, a spatial-spectral fusion. The main real imagery example, fusion of polarimetric synthetic aperture radar (SAR) with hyperspectral imagery, poses a unique challenge due to the phenomenological differences between the sensors.Theoretical models for electro-optical image formation and scene reflectivity are shown to lead naturally to a set of pixel mixing equations. Several solutions for the spatial unmixing form of these equations are examined, based on the method of least squares. In particular, a method for introducing thematic content into the solution for spatial unmixing is defined using weighted least squares. Finally, and most significantly, a spatial-spectral fusion algorithm based on the theory of projection onto convex sets (POCS) is presented. Theoretical aspects of POCS are briefly discussed, showing how the use of constraints in the form of closed convex sets drives the solution. Then, constraints are derived that are intimately tied to the underlying theoretical models. Simulated imagery is used to characterize the different constraintcombinations that can be used in a POCS-based fusion algorithm.The fusion algorithms are applied to real imagery from two data sets, a Landsat ETM+ scene over Tucson, AZ and an AVIRIS/AirSAR scene over Tombstone, AZ. The results of the fusion are analyzed using scattergrams and correlation statistics. The POCS-based fusion algorithm is shown to produce a reasonable fusion of the AVIRIS/AirSAR data, with some sharpening of spatial-spectral features.