Subpixel Target Detection in Hyperspectral Imaging Using a Deep Neural Network With a Variable Stepsize Gradient Descent Method

The main difficulty in using artificial neural networks, which are designed for classification, to detect a rare subpixel target in hyperspectral imaging is that there is typically only one actual target pixel available for training the neural networks, which require a large sample of actual target pixels to train the target class. The first current detection algorithm for subpixel target detection is based on a single-layer neural network and gradient descent method with variable stepsize to solve the optimization problem, and the second one is based on a multilayer neural network and gradient descent method with variable stepsize. The objective of this article is to extend the current algorithms by developing a detection algorithm for subpixel target detection using a deep neural network with two hidden layers and the gradient descent method with variable stepsize instead of fixed stepsize. Implementing the gradient descent method with variable stepsize can reduce computational cost by improving convergence and speed of convergence. The decision boundary is also analyzed and is linear for the single-layer neural network and nonlinear for the multilayer neural network and deep neural neural network with two hidden layers. Experimental results from two hyperspectral images, one with simulated subpixel target pixels for training and validating the algorithm and the other with simulated subpixel target pixels for training and actual subpixel target pixels for validation, have shown that the proposed algorithm can perform better than conventional algorithms, which are based on generalized likelihood ratio test.