Feed-forward neural networks to solve the closely-spaced objects problem

Abstract

We have applied a feed-forward neural network to the task of resolving closely-spaced objects (CSO). Traditional algorithmic methods are computationally expensive or numerically unstable, and techniques based on ad hoc rules are too subjective. Our approach relies on the principle that a sufficiently complex neural network can approximate an arbitrary function to an arbitrary degree of accuracy. We train a neural network to approximate the multi- dimensional function that maps from detector signal space to CSO parameter space, using an aggressive Hessian-based training algorithm and training set examples synthesized from the known inverse function. We find two important empirical results: we can simultaneously identify when the training set size is sufficient to adequately represent the mapping function, and when the network has achieved optimum generalization capability, for a given degree of network complexity. Thus we can predict the network and training set sizes necessary to achieve a given mission performance. Finally, we show how such a network can be used to provide sub-pixel resolution capabilities for missions observing both single objects and CSOs, as part of a real-time 2D sensor processor.