Anomaly Detection in Images With Smooth Background via Smooth-Sparse Decomposition

Although there are several methods for image denoising and anomaly detection, most of these perform denoising and detection sequentially, which affects detection accuracy and efficiency. Additionally, the low computational speed of some of these methods is a limitation for real-time inspection.

In this article, we develop a novel methodology for anomaly detection in noisy images with smooth backgrounds. The proposed method, named smooth-sparse decomposition, exploits regularized high-dimensional regression to decompose an image and separate anomalous regions by solving a large-scale optimization problem. To enable the proposed method for real-time implementation, a fast algorithm for solving the optimization model is proposed.