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12
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 84 (13 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.
Adaptively quadratic (AQua) image interpolation
 IEEE Transactions on Image Processing
, 2004
"... Image interpolation is a key aspect of digital image processing. This paper presents a novel interpolation method based on optimal recovery and adaptively determining the quadratic signal class from the local image behavior. The advantages of the new interpolation method are the ability to interpola ..."
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Cited by 23 (1 self)
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Image interpolation is a key aspect of digital image processing. This paper presents a novel interpolation method based on optimal recovery and adaptively determining the quadratic signal class from the local image behavior. The advantages of the new interpolation method are the ability to interpolate directly by any factor and to model properties of the data acquisition system into the algorithm itself. Through comparisons with other algorithms it is shown that the new interpolation is not only mathematically optimal with respect to the underlying image model, but visually it is very efficient at reducing jagged edges, a place where most other interpolation algorithms fail. Index Terms image modeling, quadratic classes, interpolation I.
Color LAR codec: a color image representation and compression scheme based on local resolution adjustment and selfextracting region representation
 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY
, 2007
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Demosaicing using optimal recovery
 IEEE Trans. Image Process
, 2005
"... Color images in single chip digital cameras are obtained by interpolating mosaiced color samples. These samples are encoded in a single chip CCD by sampling the light after it passes through a color filter array (CFA) that contains different color filters (i.e. red, green, and blue) placed in some p ..."
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Cited by 20 (0 self)
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Color images in single chip digital cameras are obtained by interpolating mosaiced color samples. These samples are encoded in a single chip CCD by sampling the light after it passes through a color filter array (CFA) that contains different color filters (i.e. red, green, and blue) placed in some pattern. The resulting sparsely sampled images of the threecolor planes are interpolated to obtain the complete color image. Interpolation usually introduces color artifacts due to the phaseshifted, aliased signals introduced by the sparse sampling of the CFAs. This paper introduces a nonlinear interpolation scheme based on edge information that produces high quality visual results. The new method is especially good at reconstructing the image around edges, a place where the visual human system is most sensitive.
Prediction of image detail
 in Proceedings of IEEE International Conference on Image Processing (ICIP
, 2000
"... In the problem of image interpolation, most of the difficulties arise in areas around edges and sharp changes. Around edges, many interpolation methods tend to smooth and blur image detail. Fortunately, most of the signal information is often carried around edges and areas of sharp changes and can b ..."
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Cited by 14 (0 self)
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In the problem of image interpolation, most of the difficulties arise in areas around edges and sharp changes. Around edges, many interpolation methods tend to smooth and blur image detail. Fortunately, most of the signal information is often carried around edges and areas of sharp changes and can be used to predict these missing details from a sampled image. A method for adding image detail based on the cone of influence, the evolution of the wavelet coefficients across scales, is presented in this paper. 1.
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 13 (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 ...
DirectFourier Reconstruction In Tomography And Synthetic Aperture Radar
 Intl. J. Imaging Sys. and Tech
, 1998
"... We investigate the use of directFourier (DF) image reconstruction in computerized tomography and synthetic aperture radar (SAR). One of our aims is to determine why the convolutionbackprojection (CBP) method is favored over DF methods in tomography, while DF methods are virtually always used in SAR ..."
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Cited by 9 (0 self)
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We investigate the use of directFourier (DF) image reconstruction in computerized tomography and synthetic aperture radar (SAR). One of our aims is to determine why the convolutionbackprojection (CBP) method is favored over DF methods in tomography, while DF methods are virtually always used in SAR. We show that the CBP algorithm is equivalent to DF reconstruction using a Jacobianweighted 2D periodic sinckernel interpolator. This interpolation is not optimal in any sense, which suggests that DF algorithms utilizing optimal interpolators may surpass CBP in image quality. We consider use of two types of DF interpolation: a windowed sinc kernel, and the leastsquares optimal Yen interpolator. Simulations show that reconstructions using the Yen interpolator do not possess the expected visual quality, because of regularization needed to preserve numerical stability. Next, we show that with a concentricsquares sampling scheme, DF interpolation can be performed accurately and efficiently...
Exact Interpolation and Iterative Subdivision Schemes
 IEEE Trans. Signal Processing
, 1995
"... In this paper we examine the circumstances under which a discretetime signal can be exactly interpolated given only every Mth sample. After pointing out the connection between designing an M fold interpolator and the construction of an M channel perfect reconstruction filter bank, we derive nece ..."
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Cited by 4 (1 self)
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In this paper we examine the circumstances under which a discretetime signal can be exactly interpolated given only every Mth sample. After pointing out the connection between designing an M fold interpolator and the construction of an M channel perfect reconstruction filter bank, we derive necessary and sufficient conditions on the signal under which exact interpolation is possible. Bandlimited signals are one obvious example, but numerous others exist. We examine these and show how the interpolators may be constructed. A main application is to iterative interpolation schemes, used for the efficient generation of smooth curves. We show that conventional bandlimited interpolators are not suitable in this context. We illustrate that a better criterion is to use interpolators that are exact for polynomial functions. Further, we demonstrate that these interpolators converge when iterated. We show how these may be designed for any polynomial degree N and any interpolation factor M . Th...
Signal Processing Issues In Synthetic Aperture Radar And Computer Tomography
, 1998
"... This paper also proposed another reconstruction method based on a direct approximation of the Fourier inversion formula using a twodimensional (2D) trapezoidal rule. In addition, the possibility of reconstruction from a concentricsquares raster was discussed. Numerous simple interpolators have bee ..."
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Cited by 1 (0 self)
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This paper also proposed another reconstruction method based on a direct approximation of the Fourier inversion formula using a twodimensional (2D) trapezoidal rule. In addition, the possibility of reconstruction from a concentricsquares raster was discussed. Numerous simple interpolators have been tried in DF reconstruction with the results compared with CBP [33]. In [34] and [35], the concept of angular bandlimiting was used to interpolate the polar data onto a Cartesian grid. In [36], a DF reconstruction using bilinear interpolation for diffraction tomography provided image quality that was comparable to that produced by the CBP algorithm. Very good reconstruction quality was obtained in [37] and [38] using a spline interpolator, or a hybrid type of spline interpolator. The notion of "gridding" was introduced in [39] as a method of obtaining optimal inversion of Fourier data. An optimal gridding function was proposed, and successful results were obtained when applied to the tomographic reconstruction problem. In [40], several different gridding functions were tried for DF reconstruction, and the performances were compared. In [41, 42], the linogram reconstruction method was proposed as a form of DF reconstruction. The data collection grid in the linogram method is the same as in the concentricsquares sampling scheme. The inversion of the Fourier data in [41, 42] was accomplished by first applying the chirpz transform in one direction and then computing FFTs in the other direction. In CT, many of these attempts at DF reconstruction have given a poorer result than the CBP algorithm, due to the error incurred in the process of the polartoCartesian interpolation. The attraction of DF reconstruction, however, is that it is thought to require less computation than ...
SUPERRESOLUTION USING NEURAL NETWORKS BASED ON THE OPTIMAL RECOVERY THEORY
"... An optimal recovery based neuralnetwork Super Resolution algorithm is developed. The proposed method is computationally less expensive and outputs images with high subjective quality, compared with previous neuralnetwork or optimal recovery algorithms. It is evaluated on classical SR test images wi ..."
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Cited by 1 (1 self)
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An optimal recovery based neuralnetwork Super Resolution algorithm is developed. The proposed method is computationally less expensive and outputs images with high subjective quality, compared with previous neuralnetwork or optimal recovery algorithms. It is evaluated on classical SR test images with both generic and specialized training sets, and compared with other stateoftheart methods. Results show that our algorithm is among the stateoftheart, both in quality and efficiency. 1.