Title
Direct fast method for time-limited signal reconstruction
Abbreviated Journal Title
Appl. Optics
Keywords
SINGULAR VALUE DECOMPOSITION; SPECTRAL ESTIMATION; OBJECT RESTORATION; IMAGE-RESTORATION; FOURIER-TRANSFORM; RADIATING SYSTEM; ELECTRIC FIELD; EXTRAPOLATION; SUPERRESOLUTION; BOUNDS; Optics
Abstract
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.
Journal Title
Applied Optics
Volume
45
Issue/Number
13
Publication Date
1-1-2006
Document Type
Article
Language
English
First Page
3111
Last Page
3126
WOS Identifier
ISSN
1559-128X
Recommended Citation
"Direct fast method for time-limited signal reconstruction" (2006). Faculty Bibliography 2000s. 6692.
https://stars.library.ucf.edu/facultybib2000/6692
Comments
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