Hopfield neural network based mixed pixel unmixing for multispectral data

Due to the spatial resolution limitation, mixed pixels containing energy reflected from more than one type of ground object will present, which often results in inefficiency in the quantitative analysis of the remote sensing images. To address this problem, a fully constrained linear unmixing algorithm based on Hopfield Neural Network (HNN) is proposed in this paper. The Nonnegative constraint, which has no close-form analytical solution, is secured by the activation function of neurons instead of traditional numerical method. The Sum-to-one constraint is embedded in the HNN by adopting the least square Linear Mixture Model (LMM) as the energy function. The Noise Energy Percentage (NEP) stop criterion is also proposed for the HNN to improve its robustness to various noise levels. The proposed algorithm has been compared with the widely used Fully Constrained Least Square (FCLS) algorithm and the Gradient Descent Maximum Entropy (GDME) algorithm on two sets of benchmark simulated data. The experimental results demonstrate that this novel approaches can decompose mixed pixels more accurately regardless of how much the endmember overlaps. The HNN based unmixing algorithm also shows satisfied performance in the real data experiments.