On direct methods for time-limited signal and image reconstruction and enhancement

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	On direct methods for time-limited signal and image reconstruction and enhancement
	Wang, Yanfei ; Wen, Zaiwen ; Nashed, Zuhair ; Sun, Qiyu
	2007
发表期刊	INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING
ISSN	0219-6913
卷号	5 期号:1 页码:51-68
摘要	The discrete Fourier transform (DFT) can be considered as an observing system, which has an input f, an output F, and a response with additive noise E. In many applications, part of the frequency spectrum/frequency information is missing or unavailable due to the passage of the time-limited signal through a band-limited system, for example, the discrete Fourier system. We suggest improving the resolution of the reconstruction of signals and images using a novel approach for the solution of the discrete Fourier system and by image enhancement. We note that the reconstruction of a time-limited signal can be simply realized by only using either the real part or the imaginary part of the DFT matrix. Therefore, based on the study of the special structure of the real and imaginary parts of the discrete Fourier matrix, a fast direct computational method is developed that utilizes explicit formulas for the truncated singular value decomposition (TSVD) obtained recently by the authors. For improving the resolution of the reconstructions, enhancement by logarithm transform is applied. This fast direct computational method is superior to other direct methods such as LU decomposition, QR decomposition, classical SVD and classical TSVD. The explicit TSVD along with the enhancement can be considered as a useful tool for signal and image reconstructions. Numerical tests for signal and image reconstructions and enhancements are given as well.
关键词	signal reconstruction discrete Fourier transform singular value decomposition signal and image enhancement
语种	英语
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Software Engineering ; Mathematics, Interdisciplinary Applications
WOS记录号	WOS:000250844100006
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/5253
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Yanfei
作者单位	1.Chinese Acad Sci, Inst Geol & Geophys, Beijing 100029, Peoples R China 2.State Key Lab Remote Sensing Sci, Beijing 100101, Peoples R China 3.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp, Beijing 100080, Peoples R China 4.Univ Cent Florida, Dept Math, Orlando, FL 32816 USA
推荐引用方式 GB/T 7714	Wang, Yanfei,Wen, Zaiwen,Nashed, Zuhair,et al. On direct methods for time-limited signal and image reconstruction and enhancement[J]. INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING,2007,5(1):51-68.
APA	Wang, Yanfei,Wen, Zaiwen,Nashed, Zuhair,&Sun, Qiyu.(2007).On direct methods for time-limited signal and image reconstruction and enhancement.INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING,5(1),51-68.
MLA	Wang, Yanfei,et al."On direct methods for time-limited signal and image reconstruction and enhancement".INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING 5.1(2007):51-68.