Sparse Coding with Anomaly Detection

Amir Adler, Michael Elad, Yacov Hel-Or, Ehud Rivlin

Research output: Contribution to journalArticlepeer-review


We consider the problem of simultaneous sparse coding and anomaly detection in a collection of data vectors. The majority of the data vectors are assumed to conform with a sparse representation model, whereas the anomaly is caused by an unknown subset of the data vectors—the outliers—which significantly deviate from this model. The proposed approach utilizes the Alternating Direction Method of Multipliers (ADMM) to recover simultaneously the sparse representations and the outliers components for the entire collection. This approach provides a unified solution both for jointly sparse and independently sparse data vectors. We demonstrate the usefulness of the proposed approach for irregular heartbeats detection in Electrocardiogram (ECG) as well as for specular reflectance and shadows removal from natural images.

Original languageEnglish
Pages (from-to)179-188
Number of pages10
JournalJournal of Signal Processing Systems
Issue number2
StatePublished - May 2015


  • ADMM
  • Anomaly detection
  • Arrythmia detection
  • Shadows removal
  • Sparse coding
  • Specular reflectance removal

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Modelling and Simulation
  • Hardware and Architecture


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