A Probability-Based Spectral Unmixing Analysis for Mapping Percentage Vegetation Cover of Arid and Semi-Arid Areas

China has been facing serious land degradation and desertification in its north and northwest arid and semi-arid areas. Monitoring the dynamics of percentage vegetation cover (PVC) using remote sensing imagery in these areas has become critical. However, because these areas are large, remote, and sparsely populated, and also because of the existence of mixed pixels, there have been no accurate and cost-effective methods available for this purpose. Spectral unmixing methods are a good alternative as they do not need field data and are low cost. However, traditional linear spectral unmixing (LSU) methods lack the ability to capture the characteristics of spectral reflectance and scattering from endmembers and their interactions within mixed pixels. Moreover, existing nonlinear spectral unmixing methods, such as random forest (RF) and radial basis function neural network (RBFNN), are often costly because they require field measurements of PVC from a large number of training samples. In this study, a cost-effective approach to mapping PVC in arid and semi-arid areas was proposed. A method for selection and purification of endmembers mainly based on Landsat imagery was first presented. A probability-based spectral unmixing analysis (PBSUA) and a probability-based optimized k nearest-neighbors (PBOkNN) approach were then developed to improve the mapping of PVC in Duolun County in Inner Mongolia, China, using Landsat 8 images and field data from 920 sample plots. The proposed PBSUA and PBOkNN methods were further validated in terms of accuracy and cost-effectiveness by comparison with two LSU methods, with and without purification of endmembers, and two nonlinear approaches, RF and RBFNN. The cost-effectiveness was defined as the reciprocal of cost timing relative root mean square error (RRMSE). The results showed that (1) Probability-based spectral unmixing analysis (PBSUA) was most cost-effective and increased the cost-effectiveness by 29.3% 29.3%, 33.5%, 50.8%, and 53.0% compared with two LSU methods, PBOkNN, RF, and RBFNN, respectively; (2) PBSUA, RF, and RBFNN gave RRMSE values of 22.9%, 21.8%, and 22.8%, respectively, which were not significantly different from each other at the significance level of 0.05. Compatibly, PBOkNN and LSU methods with and without purification of endmembers resulted in significantly greater RRMSE values of 27.5%, 32.4%, and 43.3%, respectively; (3) the average estimates of the sample plots and predicted maps from PBSUA, PBOkNN, RF, and RBFNN fell in the confidence interval of the test plot data, but those from two LSU methods did not, although the LSU with purification of endmembers improved the PVC estimation accuracy by 25.2% compared with the LSU without purification of endmembers. Thus, this study indicated that the proposed PBSUA had great potential for cost-effectively mapping PVC in arid and semi-arid areas.