Journal
IEEE TRANSACTIONS ON MEDICAL IMAGING
Volume 19, Issue 7, Pages 739-758Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/42.875199
Keywords
approximation constant; approximation order; B-splines; Fourier error kernel; maximal order and minimal support (Moms); piecewise-polynomials
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Based on the theory of approximation, this paper presents a unified analysis of interpolation and resampling techniques. An important issue is the choice of adequate basis functions, We show that, contrary to the common belief, those that perform best are not interpolating. By opposition to traditional interpolation, we call their use generalized interpolation; they invoice a prefiltering step when correctly applied, We explain why the approximation order inherent in any basis function is important to limit interpolation artifacts. The decomposition theorem states that any basis function endowed with approximation order can be expressed as the convolution of a B-spline of the same order with another function that has none. This motivates the use of splines and spline-based functions as a tunable way to keep artifacts in check without any significant cost penalty. We discuss implementation and performance issues, and me provide experimental evidence to support our claims.
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