Spectral unmixing

Spectral unmixing answers the question: what materials are present within a pixel, and in what proportions? A single sensor pixel typically covers an area containing several surface types simultaneously. Rather than assigning one class label to the whole pixel, linear spectral mixture analysis (LSMA) decomposes the observed reflectance spectrum into a weighted sum of pure endmember spectra, returning a fractional abundance estimate for each endmember.^[1]

The constrained least-squares formulation requires that fractional abundances are non-negative and sum to one. Endmembers commonly used in vegetation and land-cover applications are Green Vegetation (GV), Non-Photosynthetic Vegetation (NPV), Soil, and Shade, where the Shade endmember accounts for shadows and water.^[2] The INPE PRODES Brazilian Amazon deforestation monitoring system has applied Landsat 30m linear SMA annually since 1988: GV fraction images are computed, and pixels showing GV fraction loss accompanied by Soil and NPV fraction gain are classified as clearing events.^[3]

The foundational paper for linear SMA is Adams et al. 1993 (Remote Sensing of Environment), which established the endmember concept and constrained least-squares formulation.^[1] The method requires enough spectral bands to separate the endmembers of interest, with hyperspectral data providing more robust separation than multispectral for applications with many endmember types. Unmixing error increases with endmember spectral variability and degrades in highly heterogeneous landscapes where the pure-pixel assumption does not hold.