Greedy Basis Pursuit

  • Authors:
  • P.S. Huggins;S.W. Zucker

  • Affiliations:
  • HSBC, New York;-

  • Venue:
  • IEEE Transactions on Signal Processing - Part II
  • Year:
  • 2007

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Abstract

We introduce greedy basis pursuit (GBP), a new algorithm for computing sparse signal representations using overcomplete dictionaries. GBP is rooted in computational geometry and exploits equivalence between minimizing the l1-norm of the representation coefficients and determining the intersection of the signal with the convex hull of the dictionary. GBP unifies the different advantages of previous algorithms: like standard approaches to basis pursuit, GBP computes representations that have minimum l1-norm; like greedy algorithms such as matching pursuit, GBP builds up representations, sequentially selecting atoms. We describe the algorithm, demonstrate its performance, and provide code. Experiments show that GBP can provide a fast alternative to standard linear programming approaches to basis pursuit.