  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. The code is available at
\url{https://github.com/caiyu6666/AE4AD}.
