期刊
IEEE TRANSACTIONS ON SIGNAL PROCESSING
卷 55, 期 7, 页码 3760-3772出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2007.894287
关键词
computational geometry; linear programming; signal representation
We introduce greedy basis pursuit (GBP), a new algorithm for computing sparse signal representations using over-complete 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.
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