PROCEEDINGS ARTICLE | May 4, 2006

Proc. SPIE. 6233, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XII

KEYWORDS: Hyperspectral imaging, Statistical analysis, Data modeling, Sensors, Error analysis, Reflectivity, Image analysis, Atmospheric corrections, Image sensors, Atmospheric modeling

When analyzing a hyperspectral image using the linear mixture model, one makes a variety of assumptions relating to the distribution of error and the underlying mixture model. In order to test the validity of these assumptions, a simple model of hyperspectral data is examined. Generally, simple linear unmixing is performed assuming that sensor error rates are the same for each band. This assumption is violated quite easily when unmixing reflectance data. Assuming a perfect sensor, image data that perfectly obeys the linear mixture model, and perfectly known end-member spectra, the error rate for least squares linear unmixing is determinable using a simple formula. When data is transformed into reflectance, the error rates for the unmixed image increases by a significant factor due to the poor statistical normalization of the resulting data. As a means of mitigating error in unmixed imagery, two alternative unmixing methods are examined: non-negative least squares, and total least squares. Non-negative least squares can be shown to significantly outperform simple least squares, while total least squares behaves pathologically. Unmixing hyperspectral images inherently transfers error from the original hyperspectral image to the unmixed fraction plane image. Care should be taken when unmixing, so that this error is known and minimized.