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

    Authors

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

    Comments

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    Abbreviated Journal Title

    Int. J. Wavelets Multiresolut. Inf. Process.

    Keywords

    signal reconstruction; discrete Fourier transform; singular value; decomposition; signal and image enhancement; SINGULAR VALUE DECOMPOSITION; SPECTRAL ESTIMATION; OBJECT RESTORATION; FOURIER-TRANSFORM; RADIATING SYSTEM; ELECTRIC FIELD; SUPERRESOLUTION; EXTRAPOLATION; BOUNDS; Computer Science, Software Engineering; Mathematics, Interdisciplinary; Applications

    Abstract

    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.

    Journal Title

    International Journal of Wavelets Multiresolution and Information Processing

    Volume

    5

    Issue/Number

    1

    Publication Date

    1-1-2007

    Document Type

    Article

    Language

    English

    First Page

    51

    Last Page

    68

    WOS Identifier

    WOS:000250844100006

    ISSN

    0219-6913

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