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 involve 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 we provide experimental evidence to support our claims.
An Overview: From Fourier Analysis to Wavelet Analysis. The Integral Wavelet Transform and Time-Frequency Analysis. Inversion Formulas and Duals. Classification of Wavelets. Mul...
We had previously shown that regularization principles lead to approximation schemes that are equivalent to networks with one layer of hidden units, called regularization networ...
The successful application of statistical variable selection techniques to fit splines is demonstrated. Major emphasis is given to knot selection, but order determination is als...
We compare versions of six interpolation methods for the interpolation of daily precipitation, mean, minimum and maximum temperature, and sea level pressure from station data ov...
This article shows a relationship between two different approximation techniques: the support vector machines (SVM), proposed by V. Vapnik (1995) and a sparse approximation sche...
Social media, news, blog, policy document mentions