Reducing Effects of Bad Data Using Variance Based Joint Sparsity Recovery

Anne Gelb, Theresa Scarnati

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


Much research has recently been devoted to jointly sparse (JS) signal recovery from multiple measurement vectors using ℓ2 , 1 regularization, which is often more effective than performing separate recoveries using standard sparse recovery techniques. However, JS methods are difficult to parallelize due to their inherent coupling. The variance based joint sparsity (VBJS) algorithm was recently introduced in Adcock et al. (SIAM J Sci Comput, submitted). VBJS is based on the observation that the pixel-wise variance across signals convey information about their shared support, motivating the use of a weightedℓ1 JS algorithm, where the weights depend on the information learned from calculated variance. Specifically, the ℓ1 minimization should be more heavily penalized in regions where the corresponding variance is small, since it is likely there is no signal there. This paper expands on the original method, notably by introducing weights that ensure accurate, robust, and cost efficient recovery using both ℓ1 and ℓ2 regularization. Moreover, this paper shows that the VBJS method can be applied in situations where some of the measurement vectors may misrepresent the unknown signals or images of interest, which is illustrated in several numerical examples.

Original languageEnglish (US)
Pages (from-to)94-120
Number of pages27
JournalJournal of Scientific Computing
Issue number1
StatePublished - Jan 15 2019


  • False data injections
  • Image reconstruction
  • Joint sparsity
  • Multiple measurement vectors

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software
  • Numerical Analysis
  • General Engineering
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics


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