An improved algorithm for basis pursuit problem and its applications

We propose an algorithm for solving the basis pursuit problem minu∈Cn{∥u∥1:Au=f}. Our starting motivation is the algorithm for compressed sensing, proposed by Qiao, Li and Wu, which is based on linearized Bregman iteration with generalized inverse. Qiao, Li and Wu defined new algorithm for solving t...

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Bibliographic Details
Published in:Applied mathematics and computation 2019-08, Vol.355, p.385-398
Main Authors: Saha, Tanay, Srivastava, Shwetabh, Khare, Swanand, Stanimirović, Predrag S., Petković, Marko D.
Format: Article
Language:English
Subjects:
Compressive sensing
Generalized inverse
Image deblurring
Linearized Bregman iteration
Signal recovery
Sparse solution
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Summary:We propose an algorithm for solving the basis pursuit problem minu∈Cn{∥u∥1:Au=f}. Our starting motivation is the algorithm for compressed sensing, proposed by Qiao, Li and Wu, which is based on linearized Bregman iteration with generalized inverse. Qiao, Li and Wu defined new algorithm for solving the basis pursuit problem in compressive sensing using a linearized Bregman iteration and the iterative formula of linear convergence for computing the matrix generalized inverse. In our proposed approach, we combine a partial application of the Newton’s second order iterative scheme for computing the generalized inverse with the Bregman iteration. Our scheme takes lesser computational time and gives more accurate results in most cases. The effectiveness of the proposed scheme is illustrated in two applications: signal recovery from noisy data and image deblurring.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2019.02.073