A Linear Spatial Spectral Mixture Model for the Improved Estimation of Subpixel Saltcedar Cover along the Forgotten River

Abstract:

Spectral unmixing is the process of decomposing the measured spectrum of a mixed pixel into a set of pure spectral signatures called endmembers and their corresponding abundances indicating the fractional area coverage of each endmember present in the pixel. A substantial number of spectral unmixing studies rely on a spectral mixture model which assumes that spectral mixing only occurs within the extent of a pixel. However, due to adjacency effect, the spectral measurement of the pixel may be contaminated by spatial interactions from materials that are present in its spatial neighborhood. In this paper, a linear spatial spectral mixture model is developed to improve the accuracy of the estimated abundance of invasive saltcedar along the Forgotten River reach of the Rio Grande. A spatial weights matrix which specifies for each pixel the locations and the weights of its neighborhood set is used to summarize the spatial relationships among pixels in the Landsat data. A spatial lag operator, defined as a weighted average of the values at neighboring locations, is adopted as an expression of spectral contribution from nearby pixels and added to the classic linear mixture model. The fractional abundances are iteratively estimated using the alternating direction method of multipliers (ADMM) algorithm. With the incorporation of adjacency effect, RMSEs of the fractional cover of ground classes were reduced. The derived sub-pixel abundances of saltcedar are beneficial for ecological management.