We consider the problem of learning detectors with a Constant False Alarm Rate (CFAR). Classical model-based solutions to composite hypothesis testing are sensitive to imperfect models and are often computationally expensive. In contrast, data-driven machine learning is often more robust and yields classifiers with fixed computational complexity. Learned detectors usually do not have a CFAR as required in many applications. To close this gap, we introduce CFARnet where the loss function is penalized to promote similar distributions of the detector under any null hypothesis scenario. Asymptotic analysis in the case of linear models with general Gaussian noise reveals that the classical generalized likelihood ratio test (GLRT) is actually a minimizer of the CFAR constrained Bayes risk. Experiments in both synthetic data and real hyper-spectral images show that CFARnet leads to near CFAR detectors with similar accuracy as their competitors.
翻译:我们考虑的是学习检测器与常态假警报率(CFAR)的问题:基于经典模型的综合假设测试解决方案对不完善模型十分敏感,而且往往在计算上十分昂贵;相反,数据驱动的机器学习往往更加有力,并产生固定计算复杂性的分类器;为弥补这一差距,我们引入了CFARnet,其中损失功能因在任何无效假设情景下促进探测器的类似分布而受罚;对带有一般高斯噪音的线性模型的简单分析表明,典型的通用概率比测试(GLRT)实际上是CFAR限制海湾风险的最小化器;合成数据和真实超光谱图像的实验显示,CFARnet与竞争者相似的精确度接近CFAR探测器。