The autoencoder (AE) is widely utilized in deep anomaly detection, but it lacks explainability due to the complexity of nonlinear mapping. One approach to address this issue is incorporating wavelet theory, which shares similarities in decomposition and reconstruction procedures. However, the perfect reconstruction property of wavelet theory conflicts with AE-based anomaly detection. To tackle this problem, we introduce a novel deep anomaly detection method from a frequency perspective. A learnable M-band wavelet network (MWNet) is designed to offer a flexible frequency band structure for signal representation. Subsequently, with the aid of sparsity constraint, MWNet dynamically focuses on key components within each frequency band. A learnable hard threshold function with a threshold maximization constraint is proposed to retain the essential frequency band of normal signals. After training, the MWNet is exclusively capable of well reconstructing normal signals, thereby producing a noticeable reconstruction error difference between normal and abnormal signals. Extensive experiments on both simulated and experimental datasets validate the effectiveness of the proposed method. The corresponding Python codes are available at .

中文翻译：

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从频率角度进行机器异常检测的 M 波段小波网络


自动编码器（AE）广泛应用于深度异常检测，但由于非线性映射的复杂性而缺乏可解释性。解决这个问题的一种方法是结合小波理论，它在分解和重构过程上有相似之处。然而，小波理论的完美重构特性与基于AE的异常检测相冲突。为了解决这个问题，我们从频率角度引入了一种新颖的深度异常检测方法。可学习的 M 带小波网络 (MWNet) 旨在为信号表示提供灵活的频带结构。随后，借助稀疏性约束，MWNet 动态地关注每个频段内的关键组件。提出了一种具有阈值最大化约束的可学习硬阈值函数，以保留正常信号的基本频带。经过训练，MWNet 完全能够很好地重建正常信号，从而在正常信号和异常信号之间产生明显的重建误差差异。对模拟和实验数据集的大量实验验证了所提出方法的有效性。相应的 Python 代码可在 .