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

Hao Yan, Kamran Paynabar, Jianjun Shi

Research output: Contribution to journalArticlepeer-review

74 Scopus citations


In various manufacturing applications such as steel, composites, and textile production, anomaly detection in noisy images is of special importance. 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. Using simulations and a case study, we evaluate the performance of the proposed method and compare it with existing methods. Numerical results demonstrate the superiority of the proposed method in terms of the detection accuracy as well as computation time. This article has supplementary materials that includes all the technical details, proofs, MATLAB codes, and simulated images used in the article.

Original languageEnglish (US)
Pages (from-to)102-114
Number of pages13
Issue number1
StatePublished - Jan 2 2017
Externally publishedYes


  • Anomaly detection
  • Convex optimization
  • High-dimensional
  • Image
  • Regression
  • Smooth background

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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