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Reconstruction of nonuniformly sampled bandlimited signals by means of digital fractional delay filters
 IEEE Trans. Signal Processing
, 2002
"... Abstract – This paper deals with reconstruction of nonuniformly sampled bandlimited continuoustime signals using timevarying discretetime FIR filters. The points of departures are that the signal is slightly oversampled as to the average sampling frequency and that the sampling instances are know ..."
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Cited by 23 (1 self)
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Abstract – This paper deals with reconstruction of nonuniformly sampled bandlimited continuoustime signals using timevarying discretetime FIR filters. The points of departures are that the signal is slightly oversampled as to the average sampling frequency and that the sampling instances are known. Under these assumptions, a representation of the reconstructed sequence is derived that utilizes a timefrequency function. This representation enables a proper utilization of the oversampling and reduces the reconstruction problem to a design problem that resembles an ordinary filter design problem. Furthermore, for an important special case, corresponding to a certain type of periodic nonuniform sampling, it is shown that the reconstruction problem can be posed as a filterbank design problem, thus with requirements on a distortion transfer function and a number of aliasing transfer functions. 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...
Interpolation and denoising of nonuniformly sampled data using wavelet domain processing
 in Proc. IEEE Int. Conf. on Acoust., Speech, Signal Proc.  ICASSP '99
, 1999
"... In this paper, we link concepts from nonuniform sampling, smoothness function spaces, interpolation, and denoising to derive a suite of multiscale, maximumsmoothness interpolation algorithms. We formulate the interpolation problem as the optimization of finding the signal that matches the given sam ..."
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Cited by 6 (3 self)
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In this paper, we link concepts from nonuniform sampling, smoothness function spaces, interpolation, and denoising to derive a suite of multiscale, maximumsmoothness interpolation algorithms. We formulate the interpolation problem as the optimization of finding the signal that matches the given samples with smallest norm in a function smoothness space. For signals in the Besov space B, " (Lp), the optimization corresponds to convex programming in the wavelet domain; for signals in the Sobolev space We(&), the optimization reduces to a simple weighted leastsquares problem. An optional wavelet shrinkage regularization step makes the algorithm suitable for even noisy sample data, unlike classical approaches such as bandlimited and spline interpolation. 1.
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 ...
NonUniform Signaling over BandLimited Channels: A Multirate Signal Processing Approach
"... It is well known that if the communication channel is bandlimited to W Hz one can transmit at most 2W independent symbols per second. Generalized sampling theorems, nevertheless, do not restrict such a signaling to be uniform [1], [2], [3]. That is, it is theoretically possible to distribute the dat ..."
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It is well known that if the communication channel is bandlimited to W Hz one can transmit at most 2W independent symbols per second. Generalized sampling theorems, nevertheless, do not restrict such a signaling to be uniform [1], [2], [3]. That is, it is theoretically possible to distribute the data symbols nonuniformly in time as long as the average signaling rate does not exceed 2W. Since the average baud rate remains the same, nonuniform signaling techniques are rarely used in normal communication scenarios. Recently, based on the observation that almost all of the public telephone network is digital, it has been proposed that 56 kb/s transmission is theoretically possible over voice band channels [7]. The proposed signaling is a nonuniform one which makes it possible to receive independent data symbols using available 8 kHz PCM samplers while the average baud rate is kept limited to 7 kbaud (W=3500 Hz). In this report, inspired by the results given in [4], a general frame work f...
Coding of Interlaced Or Progressive Video Sources: A Theoretical Analysis.
"... This paper presents a theoretical analysis of the coding efficiency of interlaced and progressive formats for intra and prediction error images. 1 Introduction In most present sequence coding algorithms, two categories of images are considered: intra and inter images. In inter images, the motion es ..."
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This paper presents a theoretical analysis of the coding efficiency of interlaced and progressive formats for intra and prediction error images. 1 Introduction In most present sequence coding algorithms, two categories of images are considered: intra and inter images. In inter images, the motion estimation and compensation are crucial steps for the temporal decorrelation. The motion of the current image with respect to the previous decoded one is first estimated. By means of the motion vector estimates, the motion is compensated and the prediction error between the current image and its motion compensated prediction is then transformed, quantized, entropy coded and transmitted. Important refinements can be implemented. Moreover, as the displacement between successive images is not necessary a multiple of the pel distance, it has been proposed to perform estimation and compensation with subpel accuracy. In the case of progressive pictures, motion compensation with subpel accuracy is st...