Second-order statistics of stochastic spline signals
Signal Processing
Representation of High Resolution Images from Low Sampled Fourier Data: Applications to Dynamic MRI
Journal of Mathematical Imaging and Vision
Continuous time domain properties of causal cubic splines
Signal Processing
High-rate interpolation of random signals from nonideal samples
IEEE Transactions on Signal Processing
Oversampling in shift-invariant spaces with a rational sampling period
IEEE Transactions on Signal Processing
Optimized least-square nonuniform fast Fourier transform
IEEE Transactions on Signal Processing
IEEE Transactions on Image Processing
On the role of exponential splines in image interpolation
IEEE Transactions on Image Processing
Quasi-interpolation by means of filter-banks
IEEE Transactions on Signal Processing
Method of construction of two-dimensional interpolation filters
Pattern Recognition and Image Analysis
Exponential splines and minimal-support bases for curve representation
Computer Aided Geometric Design
Efficient digital pre-filtering for least-squares linear approximation
VLBV'05 Proceedings of the 9th international conference on Visual Content Processing and Representation
Rendering in shift-invariant spaces
Proceedings of Graphics Interface 2013
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We present a general Fourier-based method that provides an accurate prediction of the approximation error as a function of the sampling step T. Our formalism applies to an extended class of convolution-based signal approximation techniques, which includes interpolation, generalized sampling with prefiltering, and the projectors encountered in wavelet theory. We claim that we can predict the L2-approximation error by integrating the spectrum of the function to approximate-not necessarily bandlimited-against a frequency kernel E(ω) that characterizes the approximation operator. This prediction is easier yet more precise than was previously available. Our approach has the remarkable property of providing a global error estimate that is the average of the true approximation error over all possible shifts of the input function. Our error prediction is exact for stationary processes, as well as for bandlimited signals. We apply this method to the comparison of standard interpolation and approximation techniques. Our method has interesting implications for approximation theory. In particular, we use our results to obtain some new asymptotic expansions of the error as T→0, as well as to derive improved upper bounds of the kind found in the Strang-Fix (1971) theory. We finally show how we can design quasi-interpolators that are near optimal in the least-squares sense