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Quantitative analysis of the reconstruction performance of interpolantsThe analysis presented provides a quantitative measure of the reconstruction or interpolation performance of linear, shift-invariant interpolants. The performance criterion is the mean square error of the difference between the sampled and reconstructed functions. The analysis is applicable to reconstruction algorithms used in image processing and to many types of splines used in numerical analysis and computer graphics. When formulated in the frequency domain, the mean square error clearly separates the contribution of the interpolation method from the contribution of the sampled data. The equations provide a rational basis for selecting an optimal interpolant; that is, one which minimizes the mean square error. The analysis has been applied to a selection of frequently used data splines and reconstruction algorithms: parametric cubic and quintic Hermite splines, exponential and nu splines (including the special case of the cubic spline), parametric cubic convolution, Keys' fourth-order cubic, and a cubic with a discontinuous first derivative. The emphasis in this paper is on the image-dependent case in which no a priori knowledge of the frequency spectrum of the sampled function is assumed.
Document ID
19870013008
Acquisition Source
Legacy CDMS
Document Type
Technical Publication (TP)
Authors
Lansing, Donald L. (NASA Langley Research Center Hampton, VA, United States)
Park, Stephen K. (College of William and Mary Williamsburg, Va., United States)
Date Acquired
September 5, 2013
Publication Date
May 1, 1987
Subject Category
Numerical Analysis
Report/Patent Number
L-16164
NASA-TP-2688
NAS 1.60:2688
Accession Number
87N22441
Funding Number(s)
PROJECT: RTOP 505-60-01-01
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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