An improved algorithm for basis pursuit problem and its applications
| Autor: | Tanay Saha, Marko D. Petković, Predrag S. Stanimirović, Shwetabh Srivastava, Swanand Khare |
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| Rok vydání: | 2019 |
| Předmět: |
0209 industrial biotechnology
Deblurring Generalized inverse Applied Mathematics Partial application 020206 networking & telecommunications Basis pursuit 02 engineering and technology Image (mathematics) Computational Mathematics Matrix (mathematics) 020901 industrial engineering & automation Compressed sensing Rate of convergence 0202 electrical engineering electronic engineering information engineering Applied mathematics Mathematics |
| Zdroj: | Applied Mathematics and Computation. 355:385-398 |
| ISSN: | 0096-3003 |
| Popis: | We propose an algorithm for solving the basis pursuit problem min u ∈ C n { ∥ u ∥ 1 : A u = 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. |
| Databáze: | OpenAIRE |
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