We consider the problem of target detection with a constant false alarm rate (CFAR). This constraint is crucial in many practical applications and is a standard requirement in classical composite hypothesis testing. In settings where classical approaches are computationally expensive or where only data samples are given, Bayesian and machine learning methodologies are advantageous. CFAR is less understood in these settings. To close this gap, we introduce a framework of CFAR constrained detectors. Theoretically, we prove that a CFAR constrained Bayes optimal detector is asymptotically equivalent to the classical generalized likelihood ratio test (GLRT). Practically, we develop a deep learning framework for fitting neural networks that approximate it. Experiments in both model based target detection and data-driven hyper-spectral images demonstrates that the proposed CFARnet allows a flexible tradeoff between CFAR and accuracy. In many problems near CFAR detectors can be developed with a small loss in accuracy.

翻译：我们考虑了具有恒定虚警率（CFAR）的目标检测问题。该约束在许多实际应用中至关重要，并且是经典复合假设检验中的标准要求。在经典方法计算成本高昂或仅提供数据样本的情况下，贝叶斯和机器学习方法具有优势。在这些场景中，CFAR的理解尚不充分。为弥补这一差距，我们引入了一个CFAR约束检测器框架。理论上，我们证明了一个CFAR约束的贝叶斯最优检测器在渐近意义上等价于经典广义似然比检验（GLRT）。实际中，我们开发了一个深度学习框架，用于拟合近似该检测器的神经网络。在基于模型的目标检测和数据驱动的高光谱图像实验均表明，所提出的CFARnet能够在CFAR与精度之间实现灵活权衡。在许多问题中，可以以较小的精度损失开发出接近CFAR的检测器。