This paper addresses target discrimination in synthetic aperture radar (SAR) imagery using linear and nonlinear adaptive networks. Neural networks are extensively used for pattern classification but here the goal is discrimination. We will show that the two applications require different cost functions. We start by analyzing with a pattern recognition perspective the two-parameter constant false alarm rate (CFAR) detector which is widely utilized as a target detector in SAR. Then we generalize

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... ts principle to construct the quadratic gamma discriminator (QGD), a nonparametrically trained classifier based on local image intensity. The linear processing element of the QGD is further extended with nonlinearities yielding a multilayer perceptron (MLP) which we call the NL-QGD (nonlinear QGD). MLP's are normally trained based on the L2 norm. We experimentally show that the L2 norm is not recommended to train MLP's for discriminating targets in SAR. Inspired by the Neyman-Pearson criterion, we create a cost function based on a mixed norm to weight the false alarms and the missed detections differently. Mixed norms can easily be incorporated into the backpropagation algorithm, and lead to better performance. Several other norms (L 8 ; cross-entropy) are applied to train the NL-QGD and all outperformed the L 2 norm when validated by receiver operating characteristics (ROC) curves. The data sets are constructed from TABILS 24 ISAR targets embedded in 7 km 2 of SAR imagery (MIT/LL mission 90). Index Terms-Gamma kernels, mixed norm training, neural networks, synthetic aperture radar, target discrimination.