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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
Source PublicationINTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING
ISSN0219-6913
Volume5Issue:1Pages:51-68
AbstractThe 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.
Keywordsignal reconstruction discrete Fourier transform singular value decomposition signal and image enhancement
Language英语
WOS Research AreaComputer Science ; Mathematics
WOS SubjectComputer Science, Software Engineering ; Mathematics, Interdisciplinary Applications
WOS IDWOS:000250844100006
PublisherWORLD SCIENTIFIC PUBL CO PTE LTD
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/5253
Collection中国科学院数学与系统科学研究院
Corresponding AuthorWang, Yanfei
Affiliation1.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
Recommended Citation
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.
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