A PRECONDITIONER FOR A PRIMAL-DUAL NEWTON CONJUGATE GRADIENT METHOD FOR COMPRESSED SENSING PROBLEMS
A PRECONDITIONER FOR A PRIMAL-DUAL NEWTON CONJUGATE GRADIENT METHOD FOR COMPRESSED SENSING PROBLEMS
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DOI：
10.1137/141002062
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发表时间：
2015-01-01
影响因子：
3.1
通讯作者：
Gondzio, Jacek
中科院分区：
文献类型：
--
作者：
Dassios, Ioannis;Fountoulakis, Kimon;Gondzio, Jacek
在本文中，我们关注的压缩感知（CS）问题的解决方案，要恢复的信号是稀疏的相干和冗余字典。本文推广了[T. F. Chan，G. H. Golub，和P. Mulet，SIAM J.科学。计算：第20（1999）号来文，英文本第10页。1964年-1977年]的CS问题。我们提供了一个廉价的和可证明有效的预处理技术的线性系统使用pdNCG。CS问题的数值结果表明性能的pdNCG与建议的预条件相比，国家的最先进的现有的解决方案。
In this paper we are concerned with the solution of compressed sensing (CS) problems where the signals to be recovered are sparse in coherent and redundant dictionaries. We extend the primal-dual Newton Conjugate Gradient method (pdNCG) in [T. F. Chan, G. H. Golub, and P. Mulet, SIAM J. Sci. Comput., 20 (1999), pp. 1964-1977] to CS problems. We provide an inexpensive and provably effective preconditioning technique for linear systems using pdNCG. Numerical results are presented on CS problems which demonstrate the performance of pdNCG with the proposed preconditioner compared to state-of-the-art existing solvers.