Medical anomaly detection aims to identify abnormal findings using only normal training data, playing a crucial role in health screening and recognizing rare diseases. Reconstruction-based methods, particularly those utilizing autoencoders (AEs), are dominant in this field. They work under the assumption that AEs trained on only normal data cannot reconstruct unseen abnormal regions well, thereby enabling the anomaly detection based on reconstruction errors. However, this assumption does not always hold due to the mismatch between the reconstruction training objective and the anomaly detection task objective, rendering these methods theoretically unsound. This study focuses on providing a theoretical foundation for AE-based reconstruction methods in anomaly detection. By leveraging information theory, we elucidate the principles of these methods and reveal that the key to improving AE in anomaly detection lies in minimizing the information entropy of latent vectors. Experiments on four datasets with two image modalities validate the effectiveness of our theory. To the best of our knowledge, this is the first effort to theoretically clarify the principles and design philosophy of AE for anomaly detection. Code will be available upon acceptance.

翻译：医学异常检测旨在仅利用正常训练数据识别异常发现，在健康筛查和罕见疾病诊断中发挥着关键作用。基于重构的方法，特别是利用自编码器的方法，在该领域占据主导地位。其工作原理基于如下假设：仅在正常数据上训练的自编码器无法良好重构未见过的异常区域，从而能够根据重构误差实现异常检测。然而，由于重构训练目标与异常检测任务目标之间存在不匹配，该假设并非始终成立，导致这些方法在理论上存在缺陷。本研究致力于为基于自编码器的重构方法在异常检测中提供理论基础。通过利用信息论，我们阐明了这些方法的原理，并揭示出提升自编码器在异常检测中性能的关键在于最小化潜在向量的信息熵。在包含两种图像模态的四个数据集上的实验验证了我们理论的有效性。据我们所知，这是首次从理论上阐明自编码器用于异常检测的原理与设计理念。代码将在论文被接收后公开。