NDLI: FFT interpolation for arbitrary factors: a comparison to cubic spline interpolation and linear interpolation

Content Provider	IEEE Xplore Digital Library
Author	Hawkins, W.G.
Copyright Year	1994
Description	Author affiliation: Dept. of Radiol., Nebraska Univ., Omaha, NE, USA (Hawkins, W.G.)
Abstract	The authors applied FFT interpolation (FTI) for arbitrary factors to a common image task: 1D zoom, and compared it to cubic splines interpolation and linear interpolation. The authors also determined the relative error of the arbitrary factors FFT and the conventional FFT (integral powers of 2) for computing the Fourier transforms of trigonometric eigenfunctions. In the interpolation study, FTI proved to be satisfactory. If the data was band-limited, or nearly so, FTI was as effective as conventional interpolation. If the data was not band-limited, an anti-oscillation filter provided better results. The test data was a curve consisting of a rectangle, gaussian function and a 4th degree polynomial. The authors used interpolation to zoom the image by a factor of 3.1:1, and determined the rms (root mean square) errors by comparing the result to the known image values. To determine the relative error for computing eigenfunctions, the authors FFT'd trigonometric eigenfunctions. For an FFT of dimension 120, the relative error was less than 10/sup -10/ over a wide range of eigenvalues and compared favorably with an FFT of dimension 128, which had a relative error of less than 10/sup -13/ over the same range. The advantage of this approach is that the arbitrary factors algorithm is quite simple in design, and replaces an entire suite of FFT's based upon different prime factorizations. The authors also show that FTI is exact if the Fourier transform of the function is absolutely band-limited.
Starting Page	1433
Ending Page	1437
File Size	356983
Page Count	5
File Format	PDF
ISBN	0780325443
DOI	10.1109/NSSMIC.1994.474614
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1994-10-30
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Interpolation Spline Frequency Biomedical imaging Fourier transforms Radiology Nonlinear filters Eigenvalues and eigenfunctions Testing Polynomials
Content Type	Text
Resource Type	Article

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