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Nonuniform Fast Fourier Transforms Using MinMax Interpolation
 IEEE Trans. Signal Process
, 2003
"... The FFT is used widely in signal processing for efficient computation of the Fourier transform (FT) of finitelength signals over a set of uniformlyspaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e.,a nonuniform FT . Several pap ..."
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Cited by 121 (22 self)
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The FFT is used widely in signal processing for efficient computation of the Fourier transform (FT) of finitelength signals over a set of uniformlyspaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e.,a nonuniform FT . Several papers have described fast approximations for the nonuniform FT based on interpolating an oversampled FFT. This paper presents an interpolation method for the nonuniform FT that is optimal in the minmax sense of minimizing the worstcase approximation error over all signals of unit norm. The proposed method easily generalizes to multidimensional signals. Numerical results show that the minmax approach provides substantially lower approximation errors than conventional interpolation methods. The minmax criterion is also useful for optimizing the parameters of interpolation kernels such as the KaiserBessel function.
Analysis And Design Of MinimaxOptimal Interpolators
 IEEE Trans. Signal Proc
, 1998
"... We consider a class of interpolation algorithms, including the leastsquares optimal Yen interpolator, and we derive a closedform expression for the interpolation error for interpolators of this type. The error depends on the eigenvalue distribution of a matrix which is specified for each set of sa ..."
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Cited by 17 (3 self)
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We consider a class of interpolation algorithms, including the leastsquares optimal Yen interpolator, and we derive a closedform expression for the interpolation error for interpolators of this type. The error depends on the eigenvalue distribution of a matrix which is specified for each set of sampling points. The error expression can be used to prove that the Yen interpolator is optimal. The implementation of the Yen algorithm suffers from numerical illconditioning, forcing the use of a regularized, approximate solution. We suggest a new, approximate solution, consisting of a sinckernel interpolator with specially chosen weighting coefficients. The newly designed sinckernel interpolator is compared with the usual sinc interpolator using Jacobian (area) weighting, through numerical simulations. We show that the sinc interpolator with Jacobian weighting works well only when the sampling is nearly uniform. The newly designed sinckernel interpolator is shown to perform better than ...
Efficient Deformable Filter Banks
, 1998
"... This paper describes efficient schemes for the computation of a large number of differentely scaled/oriented filtered versions of an image. We generalize the wellknown steerable/scalable ("deformable") filter bank structure by imposing XY separability on the basis filters. The resulting ..."
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Cited by 9 (0 self)
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This paper describes efficient schemes for the computation of a large number of differentely scaled/oriented filtered versions of an image. We generalize the wellknown steerable/scalable ("deformable") filter bank structure by imposing XY separability on the basis filters. The resulting systems, designed by an iterative projections technique, achieve substantial reduction of the computational cost. To reduce the memory requirement, we adopt a multirate implementation. The resulting structure, however, is not shiftinvariant. We introduce a design criterion for multirate deformable structures that jointly controls the approximation error and the shiftvariance. 1 Introduction Elementary visual structures such as lines, edges, texture, motion, are powerful "cues" to understand the structure of the outside world from its visual appearance (the image), and their identification is instrumental for almost any visual task. Classical image processing problems (enhancement, denoising) may al...
Signal Processing Issues In Synthetic Aperture Radar And Computer Tomography
, 1998
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Optimal Design Of Multirate Systems
, 1995
"... ... approximation error over traditional design techniques is obtained. Finally, the design of cascade systems is considered. Optimal designs for these systems are found to provide additional reduction in computational complexity. ..."
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... approximation error over traditional design techniques is obtained. Finally, the design of cascade systems is considered. Optimal designs for these systems are found to provide additional reduction in computational complexity.
Efficient Deformable Filter Banks
 IEEE Trans. Signal Processing
, 1998
"... This correspondence describes efficient schemes for the computation of a large number of differently scaled/oriented filtered versions of an image. We generalize the wellknown steerable/scalable ("deformable") filter bank structure by imposing XY separability on the basis filters. The re ..."
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This correspondence describes efficient schemes for the computation of a large number of differently scaled/oriented filtered versions of an image. We generalize the wellknown steerable/scalable ("deformable") filter bank structure by imposing XY separability on the basis filters. The resulting systems, designed by an iterative projections technique, achieve substantial reduction of the computational cost.
and Doug Shy
, 1997
"... This paper describes ecient schemes for the computation of a large number of dierentely scaled/oriented ltered versions of an image. We generalize the wellknown steerable/scalable (\deformable") lter bank structure by imposing XY separability on the basis lters. The resulting systems, design ..."
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This paper describes ecient schemes for the computation of a large number of dierentely scaled/oriented ltered versions of an image. We generalize the wellknown steerable/scalable (\deformable") lter bank structure by imposing XY separability on the basis lters. The resulting systems, designed by an iterative projections technique, achieve substantial reduction of the computational cost. To reduce the memory requirement, we adopt a multirate implementation. The resulting structure, however, is not shiftinvariant. We introduce a design criterion for multirate deformable structures that jointly controls the approximation error and the shiftvariance. 1
Analysis and Design of
"... Abstract — We consider a class of interpolation algorithms, including the leastsquares optimal Yen interpolator, and we derive a closedform expression for the interpolation error for interpolators of this type. The error depends on the eigenvalue distribution of a matrix that is specified for each ..."
Abstract
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Abstract — We consider a class of interpolation algorithms, including the leastsquares optimal Yen interpolator, and we derive a closedform expression for the interpolation error for interpolators of this type. The error depends on the eigenvalue distribution of a matrix that is specified for each set of sampling points. The error expression can be used to prove that the Yen interpolator is optimal. The implementation of the Yen algorithm suffers from numerical ill conditioning, forcing the use of a regularized, approximate solution. We suggest a new, approximate solution consisting of a sinckernel interpolator with specially chosen weighting coefficients. The newly designed sinckernel interpolator is compared with the usual sinc interpolator using Jacobian (area) weighting through numerical simulations. We show that the sinc interpolator with Jacobian weighting works well only when the sampling is nearly uniform. The newly designed sinckernel interpolator is shown to perform better than the sinc interpolator with Jacobian weighting. I.