Demeaned Sparse: Efficient Anomaly Detection by Residual Estimate

Frequency-domain image anomaly detection methods can substantially enhance anomaly detection performance, however, they still lack an interpretable theoretical framework to guarantee the effectiveness of the detection process. We propose a novel test to detect anomalies in structural image via a Demeaned Fourier transform (DFT) under factor model framework, and we proof its effectiveness. We also briefly give the asymptotic theories of our test, the asymptotic theory explains why the test can detect anomalies at both the image and pixel levels within the theoretical lower bound. Based on our test, we derive a module called Demeaned Fourier Sparse (DFS) that effectively enhances detection performance in unsupervised anomaly detection tasks, which can construct masks in the Fourier domain and utilize a distribution-free sampling method similar to the bootstrap method. The experimental results indicate that this module can accurately and efficiently generate effective masks for reconstruction-based anomaly detection tasks, thereby enhancing the performance of anomaly detection methods and validating the effectiveness of the theoretical framework.

Imagine you’re trying to spot a tiny crack in a huge glass window or a small flaw in a complicated machine part just by looking at a photo. Detecting such subtle anomalies in images is really important for things like quality control or medical checks. Some advanced methods analyze images by breaking them down into waves and frequencies—kind of like how a music equalizer splits sound into different tones—to find these unusual patterns.However, these frequency-based methods often don’t have a clear explanation for why they work so well. In our research, we developed a new test that uses a special mathematical “lens,” called the Demeaned Fourier Transform, to highlight anomalies in images. We also explain the theory behind it, showing why this test can catch problems both in the big picture and down to tiny details, almost as well as theoretically possible.Building on this, we created a module called Demeaned Fourier Sparse (DFS) that improves anomaly detection without the need for any prior knowledge of abnormal images. It works by smartly selecting parts of the image in the frequency world, like focusing on certain musical notes to find the source of a strange sound. Our tests show that DFS can quickly and accurately create masks, making anomaly detection more reliable and effective.