Title

On Direct Methods For Time-Limited Signal And Image Reconstruction And Enhancement

Keywords

Discrete Fourier transform; Signal and image enhancement; Signal reconstruction; Singular value decomposition

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. © 2007 World Scientific Publishing Company.

Publication Date

1-1-2007

Publication Title

International Journal of Wavelets, Multiresolution and Information Processing

Volume

5

Issue

1

Number of Pages

51-68

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1142/S0219691307001574

Socpus ID

33846300698 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/33846300698

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