Sinc interpolation of discrete periodic signals

Schanze, Thomas

doi:10.1109/78.388863

Cited by 93 publications

(45 citation statements)

References 2 publications

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“…Consequently, it is impossible to retrieve the original images exactly from the resulting samples by means of sinc interpolation. Another problem of sinc interpolation is the fact that, since the sinc function has infinite support, (2) cannot be computed in practice, except in the case of periodic images [46], which are not likely to occur in medical imaging. Furthermore, interpolation by means of a band-limiting convolution kernel may result in Gibbs phenomena, which are very disturbing in images.…”

Section: Pp-3mentioning

confidence: 99%

Quantitative evaluation of convolution-based methods for medical image interpolation

Meijering

Niessen

Viergever

2001

Medical Image Analysis

254

165

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Abstract-Interpolation is required in a variety of medical image processing applications. Although many interpolation techniques are known from the literature, evaluations of these techniques for the specific task of applying geometrical transformations to medical images are still lacking. In this paper we present such an evaluation. We consider convolution-based interpolation methods and rigid transformations (rotations and translations). A large number of sincapproximating kernels are evaluated, including piecewise polynomial kernels and a large number of windowed sinc kernels, with spatial supports ranging from two to ten grid intervals. In the evaluation we use images from a wide variety of medical image modalities. The results show that spline interpolation is to be preferred over all other methods, both for its accuracy and its relatively low computational cost.

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Section: Pp-3mentioning

confidence: 99%

Quantitative evaluation of convolution-based methods for medical image interpolation

Meijering

Niessen

Viergever

2001

Medical Image Analysis

254

165

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show abstract

“…It will also lead to efficient filter and filterbank structures for reconstruction from uniform and recurrent nonuniform samples, as we show in Sections V and VI. The set of reconstruction functions for uniform samples was first treated by Cauchy [1] and later by Stark [27], Brown [30], and Schanze [29] in different ways. Reconstruction from any even number of uniform samples was considered in [28] and [29].…”

Section: Reconstruction From Nonuniform Samplesmentioning

confidence: 99%

“…The set of reconstruction functions for uniform samples was first treated by Cauchy [1] and later by Stark [27], Brown [30], and Schanze [29] in different ways. Reconstruction from any even number of uniform samples was considered in [28] and [29]. As we show in Section V, these results are all special cases of Theorem 1 derived in this section.…”

Section: Reconstruction From Nonuniform Samplesmentioning

confidence: 99%

Nonuniform Sampling of Periodic Bandlimited Signals

Margolis

Eldar

2008

IEEE Trans. Signal Process.

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Abstract-Digital processing techniques are based on representing a continuous-time signal by a discrete set of samples. This paper treats the problem of reconstructing a periodic bandlimited signal from a finite number of its nonuniform samples. In practical applications, only a finite number of values are given. Extending the samples periodically across the boundaries, and assuming that the underlying continuous time signal is bandlimited, provides a simple way to deal with reconstruction from finitely many samples. Two algorithms for reconstructing a periodic bandlimited signal from an even and an odd number of nonuniform samples are developed. In the first, the reconstruction functions constitute a basis while in the second, they form a frame so that there are more samples than needed for perfect reconstruction. The advantages and disadvantages of each method are analyzed. Specifically, it is shown that the first algorithm provides consistent reconstruction of the signal while the second is shown to be more stable in noisy environments. Next, we use the theory of finite dimensional frames to characterize the stability of our algorithms. We then consider two special distributions of sampling points: uniform and recurrent nonuniform, and show that for these cases, the reconstruction formulas as well as the stability analysis are simplified significantly. The advantage of our methods over conventional approaches is demonstrated by numerical experiments.

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“…This is not the case for periodic signals since both optimal reconstruction and measurement of the sampling error is possible using only the samples of one period. In [23], Schanze deduced a finite support Shannon kernel for periodic signals. This particular case will be detailed here, considering the polar contour development around an internal origin as a periodic continuous signal.…”

Section: Shannon Interpolation Kernel For Periodic Functionsmentioning

confidence: 99%

“…The reconstruction is reduced to N samples {ρ n }, distributed in a period that corresponds to a complete rotation of the polar angle, using the Shannon kernel for periodic functions [23]:…”

Section: Shannon Interpolation Kernel For Periodic Functionsmentioning

confidence: 99%