Direct fast method for time-limited signal reconstruction

    Authors

    Y. F. Wang; Z. W. Wen; Z. Nashed;Q. Y. Sun

    Comments

    Authors: contact us about adding a copy of your work at STARS@ucf.edu

    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

    WOS:000237143800029

    ISSN

    1559-128X

    Share

    COinS