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12
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 51 (8 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 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 ...
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 10 (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 9 (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.
Reconstruction of periodically nonuniformly sampled bandlimited signals using timevarying FIR filters
 In Proc. Fourth Int. Workshop Spectral Methods Multirate Signal Processing
, 2004
"... This paper deals with reconstruction of nonuniformly sampled bandlimited continuoustime signals using timevarying discretetime FIR filters. The point of departure is a representation of the reconstructed sequence that utilizes a timefrequency function. This representation enables a proper utiliz ..."
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Cited by 3 (1 self)
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This paper deals with reconstruction of nonuniformly sampled bandlimited continuoustime signals using timevarying discretetime FIR filters. The point of departure is a representation of the reconstructed sequence that utilizes a timefrequency function. This representation enables a proper utilization of the slight oversampling that is assumed and reduces the reconstruction problem to a design problem that resembles an ordinary filter design problem. Of particular interest in this paper is an important special case of nonuniform sampling that corresponds to a certain type of periodic nonuniform sampling. It is shown how the reconstruction problem in this case can be posed as a multirate filterbank design problem, thus with requirements on a distortion transfer function and a number of aliasing transfer functions. (a) (c) x a(t)
Signal Processing Issues In Synthetic Aperture Radar And Computer Tomography
, 1998
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Statistical Properties of Coded Interlaced and Progressive Image Sequences
"... In the present paper, we investigate the statistical properties of interlaced and progressive image sequences in order to determine what is the most efficient format from a coding point of view. Intra and inter coding modes are both considered. The main result is that, for both intra and inter image ..."
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Cited by 1 (0 self)
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In the present paper, we investigate the statistical properties of interlaced and progressive image sequences in order to determine what is the most efficient format from a coding point of view. Intra and inter coding modes are both considered. The main result is that, for both intra and inter images, the coding of progressive images outperforms the coding of interlaced ones for low bitrates and large motion vectors. Particular attention is paid to inter coding with subpel accuracy, where the effects of non ideal interpolation filters and finite precision of the motion vector are taken into account. This author would like to thank the Belgian NSF for its financial support 1 Introduction In most present sequence coding algorithms, two categories of images are considered: intra and inter images. This is the case for the popular MPEG 2 coding algorithm [1, 2]. In intra images, no temporal decorrelation is performed. They are used as periodical refresh and as entry points in the sequ...
Multiband signal reconstruction from finite samples*
, 1994
"... The minimum meansquared error (MMSE) estimator has been used to reconstruct a bandlimited signal from its finite samples in a bounded interval and shown to have many nice properties. In this research, we consider a special class of bandlimited 1D and 2D signals which have a multiband structure ..."
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The minimum meansquared error (MMSE) estimator has been used to reconstruct a bandlimited signal from its finite samples in a bounded interval and shown to have many nice properties. In this research, we consider a special class of bandlimited 1D and 2D signals which have a multiband structure in the frequency domain, and propose a new reconstruction algorithm to exploit the multiband feature of the underlying signals. The concept of the critical value and region is introduced to measure the performance of a reconstruction algorithm. We show analytically that the new algorithm performs #better than the MMSE estimator for bandlimited/multiband signals in terms of the critical value and region measure. Finally, numerical examples of 1D and 2D signal reconstruction are given for performance comparison of various methods.
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...
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...