Direct fast method for time-limited signal reconstruction

Applied Optics
Yanfei WangQiyu Sun

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.

References

Nov 1, 1988·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·X HuT Spraggins
Feb 6, 2008·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·M Cetin, W C Karl
Feb 16, 2008·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·S R DeGraaf
Sep 1, 1975·Applied Optics·T S Huang, P M Narendra
May 15, 1979·Applied Optics·N N Abdelmalek, T Kasvand
Dec 15, 1981·Applied Optics·N N AbdelmalekM M Tremblay

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