## Greedy Basis Pursuit (2006)

Citations: | 7 - 0 self |

### BibTeX

@MISC{Huggins06greedybasis,

author = {Patrick S. Huggins and Steven W. Zucker},

title = {Greedy Basis Pursuit},

year = {2006}

}

### OpenURL

### Abstract

We introduce Greedy Basis Pursuit (GBP), a new algorithm for computing signal representations using overcomplete dictionaries. GBP is rooted in computational geometry and exploits an equivalence between minimizing the ℓ 1-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 ℓ 1-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.