Nonlinear estimation of subpixel proportion via kernel least square regression

Spectral mixture analysis is an efficient approach to spectral decomposition of hyperspectral remotely sensed imagery, using land cover proportions which can be estimated from pixel values through model inversion. In this paper, a kernel least square regression algorithm has been developed for nonlinear approximation of subpixel proportions. This procedure includes two steps. The first step is to select the feature vectors by defining a global criterion to characterize the image data structure in the feature space and the second step is the projection of pixels onto the feature vectors and the application of classical linear regressive algorithm. Experiments using simulated data, synthetic data and Enhanced Thematic Mapper (ETM) + data have been carried out, and the results demonstrate that the proposed method can improve proportion estimation. By using the simulated and synthetic data, over 85% of the total pixels in the image are found to lie between the 10% difference lines, and the root mean square error (RMSE) is less than 0.09. Using the real data, the proposed method can also perform satisfactorily with an average RMSE of about 0.12. This algorithm was also compared with other widely used kernel based algorithms, i.e. support vector regression and radial basis function neutral network and the results show that the proposed algorithm outperforms other algorithms about 5% in subpixel proportion estimation.