The presence of mixed pixels (containing more than one material) is unavoidable in remotely sensed hyperspectral data. They adversely affect the results of analysis algorithms developed for different remote sensing applications such as target detection and landcover mapping. Therefore, there is a need to extract subpixel level information. To fulfill this requirement, the field of spectral unmixing has been developed. Spectral unmixing is a two-step process: First, the pure materials, or endmembers, which are present in the scene are identified. Next, the fractional presence, or abundance, of each of these materials within each pixel is derived. Most unmixing algorithms are based on the linear mixing assumption, which considers a pixel spectrum as a convex linear combination of endmember spectra weighted by their corresponding abundances.

In this work, the fractional abundances of known endmembers are estimated using geometry based approaches. These geometry based unmixing algorithms utilize the concepts of convex geometry and solve the problem by projecting the data onto a closest point inside the simplex spanned by the endmembers. The simplex is first constructed as an intersection of planes and half-spaces. Then, the Dykstra alternating projection algorithm is used to find the closest point projection onto this intersection.

Furthermore, new techniques for some specific remote sensing applications such as subpixel target detection and subpixel landcover mapping, which are strongly related to spectral unmixing, are also developed. In target detection, the concepts of geometry based spectral unmixing and a matched filter are combined. By considering the target as one of the endmembers, the simplex projection method is used to identify background pixels, which are then used to calculate the background statistics required for the matched filter. In subpixel mapping, a high resolution classification map is obtained using the spectral unmixing results. To improve the classification results, a spatial association statistic (Getis index) and extra information in the form of labeled segments from a high resolution color image are used.