Direct fast method for time-limited signal reconstruction

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	Direct fast method for time-limited signal reconstruction
	Wang, YF ; Wen, ZW ; Nashed, Z ; Sun, QY
	2006-05-01
发表期刊	APPLIED OPTICS
ISSN	1559-128X
卷号	45 期号:13 页码:3111-3126
摘要	We consider reconstruction of signals by a direct method for the solution of the discrete Fourier system. We note that the reconstruction of a time-limited signal can be simply realized by using only either the real part or the imaginary part of the discrete Fourier transform (DFT) matrix. Therefore, based on the study of the special structure of the real and imaginary parts of the discrete Fourier matrix, we propose a fast direct method for the signal reconstruction problem, which utilizes the numerically truncated singular value decomposition. The method enables us to recover the original signal in a stable way from the frequency information, which may be corrupted by noise and/or some missing data. The classical inverse Fourier transform cannot be applied directly in the latter situation. The pivotal point of the reconstruction is the explicit computation of the singular value decomposition of the real part of the DFT for any order. Numerical experiments for 1D and 2D signal reconstruction and image restoration are given. (c) 2006 Optical Society of America.
语种	英语
WOS研究方向	Optics
WOS类目	Optics
WOS记录号	WOS:000237143800029
出版者	OPTICAL SOC AMER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/2403
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, YF
作者单位	1.State Key Lab Remote Sensing Sci, Beijing 100101, Peoples R China 2.Univ Cent Florida, Dept Math, Orlando, FL 32816 USA 3.Chinese Acad Sci, State Key Lab Sci & Engn Comp, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Wang, YF,Wen, ZW,Nashed, Z,et al. Direct fast method for time-limited signal reconstruction[J]. APPLIED OPTICS,2006,45(13):3111-3126.
APA	Wang, YF,Wen, ZW,Nashed, Z,&Sun, QY.(2006).Direct fast method for time-limited signal reconstruction.APPLIED OPTICS,45(13),3111-3126.
MLA	Wang, YF,et al."Direct fast method for time-limited signal reconstruction".APPLIED OPTICS 45.13(2006):3111-3126.