Please use this identifier to cite or link to this item:
|Title:||Linearized Bregman iterations for compressed sensing||Authors:||Cai, J.-F.
|Issue Date:||Jul-2009||Citation:||Cai, J.-F., Osher, S., Shen, Z. (2009-07). Linearized Bregman iterations for compressed sensing. Mathematics of Computation 78 (267) : 1515-1536. ScholarBank@NUS Repository. https://doi.org/10.1090/S0025-5718-08-02189-3||Abstract:||Finding a solution of a linear equation Au = f with various minimization properties arises from many applications. One such application is compressed sensing, where an efficient and robust-to-noise algorithm to find a minimal ℓ 1 norm solution is needed. This means that the algorithm should be tailored for large scale and completely dense matrices A, while Au and A T u can be computed by fast transforms and the solution we seek is sparse. Recently, a simple and fast algorithm based on linearized Bregman iteration was proposed in [28,32] for this purpose. This paper is to analyze the convergence of linearized Bregman iterations and the minimization properties of their limit. Based on our analysis here, we derive also a new algorithm that is proven to be convergent with a rate. Furthermore, the new algorithm is simple and fast in approximating a minimal ℓ 1 norm solution of Au = f as shown by numerical simulations. Hence, it can be used as another choice of an efficient tool in compressed sensing. © 2008 American Mathematical Society.||Source Title:||Mathematics of Computation||URI:||http://scholarbank.nus.edu.sg/handle/10635/115795||ISSN:||00255718||DOI:||10.1090/S0025-5718-08-02189-3|
|Appears in Collections:||Staff Publications|
Show full item record
Files in This Item:
There are no files associated with this item.
checked on Oct 13, 2021
WEB OF SCIENCETM
checked on Oct 6, 2021
checked on Oct 14, 2021
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.