Optimized least-square nonuniform fast Fourier transform
IEEE Transactions on Signal Processing
Efficient NUFFT algorithm for non-Cartesian MRI reconstruction
ISBI'09 Proceedings of the Sixth IEEE international conference on Symposium on Biomedical Imaging: From Nano to Macro
Fast and accurate Gaussian derivatives based on B-splines
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Exponential splines and minimal-support bases for curve representation
Computer Aided Geometric Design
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We present an exact expression for the L2 error that occurs when one approximates a periodic signal in a basis of shifted and scaled versions of a generating function. This formulation is applicable to a wide variety of linear approximation schemes including wavelets, splines, and bandlimited signal expansions. The formula takes the simple form of a Parseval's-like relation, where the Fourier coefficients of the signal are weighted against a frequency kernel that characterizes the approximation operator. We use this expression to analyze the behavior of the error as the sampling step approaches zero. We also experimentally verify the expression of the error in the context of the interpolation of closed curves