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The In-Crowd Algorithm for Fast Basis Pursuit Denoising

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3 Author(s)
Gill, P.R. ; Sch. of Electr. & Comput. Eng., Cornell Univ., Ithaca, NY, USA ; Wang, A. ; Molnar, A.

We introduce a fast method, the “in-crowd” algorithm, for finding the exact solution to basis pursuit denoising problems. The in-crowd algorithm discovers a sequence of subspaces guaranteed to arrive at the support set of the final solution of l1 -regularized least squares problems. We provide theorems showing that the in-crowd algorithm always converges to the correct global solution to basis pursuit denoising problems. We show empirically that the in-crowd algorithm is faster than the best alternative solvers (homotopy, fixed point continuation and spectral projected gradient for l1 minimization) on certain well- and ill-conditioned sparse problems with more than 1000 unknowns. We compare the in-crowd algorithm's performance in high- and low-noise regimes, demonstrate its performance on more dense problems, and derive expressions giving its computational complexity.

Published in:

Signal Processing, IEEE Transactions on  (Volume:59 ,  Issue: 10 )

Date of Publication:

Oct. 2011

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