计算机科学 ›› 2013, Vol. 40 ›› Issue (Z6): 93-95.
戚平
QI Ping
摘要: 由于允许从少量数据中恢复原始信号的压缩感知的引入,基于1范数正则化的最优化方法近来越来越受到重视。利用最小二乘问题的一种等价形式和Bregman迭代方法的一些技巧,本文推导出了可以用于稀疏信号重构求解的非满秩情况下的A+线性Bregman迭代方法的一种新的等价形式,并证明了它与原形式的等价性。
[1] Chen S S,Donoho D L,Saunders M A.Atomic decomposition by basis pursuit[J].SIAM J.Sci.Comput,1998,20:33-61 [2] Candes E,Romberg J,Tao T.Robust uncertainty principles:exact signal reconstruction from highly incomplete frequency information[J].IEEE Trans.Inform.Theory,2006,52:489-509 [3] Donoho D L.Compressed Sensing[J].IEEE Trans.Inform.Theory,2006,52:1289-1306 [4] Hale E,Yin W,Zhang Y.A Fixed-Point Continuation Method for L1-Regularization with Application to Compressed Sensing[R].CAAM Technical Report tr07-07.Rice University,Houston,TX,2007 [5] Yin W,Osher S,Goldfarb D,et al.Bregman iterative algorithms for 1-Regularization with Application to Compressed Sensing [J].SIAM J.Imaging Sciences, 2008,1:143-168 [6] Cai J F,Chan R H,Shen Z.Linearizad Bregman iterations forcompresses sensing[J].Math.Comp.,2009,78(267):1515-1536 [7] Cai J F,Osher S,Shen S W.Linearized Bregman Iteration for Frame-Based Image Deblurring[J].SIAM J.Imaging Sciences,2009,2(1):226-252 [8] 张慧,成礼智.A-线性Bregman迭代算法[J].计算数学,2010,32(1):97-104 [9] Ben-Israel A,Greville T N E.Generalized inverses:Theory and Applications(2nd ed)[M].New York,NY:Springer,2003:35-130 [10] Osher S,Mao Y,Dong B,et al.Fast Linearized Bregman Iteration for Compressed Sensing and Sparse Denoising[R].Report 08-37,UCLA.CAM,2008:1-18 [11] Donoho D L.Denoising by softthresholding[J].IEEE Trans.Inform.Theory,1995,3:613-627 |
No related articles found! |
|