• Corpus ID: 18762409

Inding a General Mechanism for Switching Be- Ieee Signal Processing Magazine Spline Interpolation November 1999 Ieee Signal Processing Magazine Ieee Signal Processing Magazine November 1999 Cubic 6-spline Basis Functlons Cardinal Splines

@inproceedings{IndingAG,
  title={Inding a General Mechanism for Switching Be- Ieee Signal Processing Magazine Spline Interpolation November 1999 Ieee Signal Processing Magazine Ieee Signal Processing Magazine November 1999 Cubic 6-spline Basis Functlons Cardinal Splines},
  author={}
}
  • Computer Science
tween the continuous and discrete signal domains is one ofthe fundamental issues in signal processing. It is a question that arises naturally during the acquisition process where an analog signal or The textbook approach to those problems is provided by Shannon's sampling theory, which describes an equivalence between a band-limited function and its equidis-tant samples taken at a frequency that is superior or equal to the Nyquist rate 1761. Even though this theory has had-_. . ~. image-is to… 

References

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Polynomial spline signal approximations: Filter design and asymptotic equivalence with Shannon's sampling theorem
TLDR
This work has shown that the B-spline interpolation of order 2n+1 of the sampled filtered sequence are identical to the coefficients of the least-squares approximation of g(t) of order n, which confirms the parallel with the classical sampling/reconstruction procedure for bandlimited signals.
Quadratic spline interpolator
A simple system is proposed which generates a quadratic spline function interpolating a given discrete-time signal. It works as a D-A converter which is free from phase distortions and whose output
Quantitative Fourier analysis of approximation techniques. II. Wavelets
  • T. Blu, M. Unser
  • Mathematics, Computer Science
    IEEE Trans. Signal Process.
  • 1999
TLDR
A general Fourier method that provides an accurate prediction of the approximation error, irrespective of the scaling properties of the approximating functions is proposed, and sharp, asymptotically optimal upper bounds for the least-squares approximation error are computed.
Quantitative Fourier analysis of approximation techniques. I. Interpolators and projectors
TLDR
It is shown how to design quasi-interpolators that are near optimal in the least-squares sense, and 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.
Fractional Splines and Wavelets
TLDR
The symmetric version of the B-splines can be obtained as the solution of a variational problem involving the norm of a fractional derivative, and may be used to build new families of wavelet bases with a continuously varying order parameter.
Comparison of Interpolating Methods for Image Resampling
When resampling an image to a new set of coordinates (for example, when rotating an image), there is often a noticeable loss in image quality. To preserve image quality, the interpolating function
Shift-orthogonal wavelet bases using splines
TLDR
Examples of a new type of wavelet basis functions that are orthogonal across shifts but not across scales are presented, which may be useful for image coding applications.
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