Results 1  10
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71
Splines: A Perfect Fit for Signal/Image Processing
 IEEE SIGNAL PROCESSING MAGAZINE
, 1999
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Extraction of HighResolution Frames from Video Sequences
 IEEE Transactions on Image Processing
, 1996
"... The human visual system appears to be capable of temporally integrating information in a video sequence in such a way that the perceived spatial resolution of a sequence appears much higher than the spatial resolution of an individual frame. While the mechanisms in the human visual system which do t ..."
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Cited by 211 (10 self)
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The human visual system appears to be capable of temporally integrating information in a video sequence in such a way that the perceived spatial resolution of a sequence appears much higher than the spatial resolution of an individual frame. While the mechanisms in the human visual system which do this are unknown, the effect is not too surprising given that temporally adjacent frames in a video sequence contain slightly different, but unique, information. This paper addresses how to utilize both the spatial and temporal information present in a short image sequence to create a single highresolution video frame. A novel observation model based on motion compensated subsampling is proposed for a video sequence. Since the reconstruction problem is illposed, Bayesian restoration with a discontinuitypreserving prior image model is used to extract a highresolution video still given a short lowresolution sequence. Estimates computed from a lowresolution image sequence containing a subp...
Sampling—50 years after Shannon
 Proceedings of the IEEE
, 2000
"... This paper presents an account of the current state of sampling, 50 years after Shannon’s formulation of the sampling theorem. The emphasis is on regular sampling, where the grid is uniform. This topic has benefited from a strong research revival during the past few years, thanks in part to the math ..."
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Cited by 207 (22 self)
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This paper presents an account of the current state of sampling, 50 years after Shannon’s formulation of the sampling theorem. The emphasis is on regular sampling, where the grid is uniform. This topic has benefited from a strong research revival during the past few years, thanks in part to the mathematical connections that were made with wavelet theory. To introduce the reader to the modern, Hilbertspace formulation, we reinterpret Shannon’s sampling procedure as an orthogonal projection onto the subspace of bandlimited functions. We then extend the standard sampling paradigm for a representation of functions in the more general class of “shiftinvariant” functions spaces, including splines and wavelets. Practically, this allows for simpler—and possibly more realistic—interpolation models, which can be used in conjunction with a much wider class of (antialiasing) prefilters that are not necessarily ideal lowpass. We summarize and discuss the results available for the determination of the approximation error and of the sampling rate when the input of the system is essentially arbitrary; e.g., nonbandlimited. We also review variations of sampling that can be understood from the same unifying perspective. These include wavelets, multiwavelets, Papoulis generalized sampling, finite elements, and frames. Irregular sampling and radial basis functions are briefly mentioned. Keywords—Bandlimited functions, Hilbert spaces, interpolation, least squares approximation, projection operators, sampling,
The Connection between Regularization Operators and Support Vector Kernels
, 1998
"... In this paper a correspondence is derived between regularization operators used in Regularization Networks and Support Vector Kernels. We prove that the Green's Functions associated with regularization operators are suitable Support Vector Kernels with equivalent regularization properties. Moreover ..."
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Cited by 146 (43 self)
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In this paper a correspondence is derived between regularization operators used in Regularization Networks and Support Vector Kernels. We prove that the Green's Functions associated with regularization operators are suitable Support Vector Kernels with equivalent regularization properties. Moreover the paper provides an analysis of currently used Support Vector Kernels in the view of regularization theory and corresponding operators associated with the classes of both polynomial kernels and translation invariant kernels. The latter are also analyzed on periodical domains. As a byproduct we show that a large number of Radial Basis Functions, namely conditionally positive definite functions, may be used as Support Vector kernels.
BSpline Signal Processing: Part ITheory
 IEEE Trans. Signal Processing
, 1993
"... This paper describes a set of efficient filtering techniques for the processing and representation of signals in terms of continuous Bspline basis functions. We first consider the problem of determining the spline coefficients for an exact signal interpolation (direct Bspline transform). The rever ..."
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Cited by 116 (24 self)
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This paper describes a set of efficient filtering techniques for the processing and representation of signals in terms of continuous Bspline basis functions. We first consider the problem of determining the spline coefficients for an exact signal interpolation (direct Bspline transform). The reverse operation is the signal reconstruction from its spline coefficients with an optional zooming factor rn (indirect Bspline transform) . We derive general expressions for the z transforms and the equivalent continuous impulse responses of Bspline interpolators of order n. We present simple techniques for signal differentiation and filtering in the transformed domain. We then derive recursive filters that efficiently solve the problems of smoothing spline and least squares approximations. The smoothing spline technique approximates a signal with a complete set of coefficients subject to certain regularization or smoothness constraints. The least squares approach, on the other hand, uses a reduced number of Bspline coefficients with equally spaced nodes; this technique is in many ways analogous to the application of antialiasing lowpass filter prior to decimation in order to represent a signal correctly with a reduced number of samples.
Survey: Interpolation Methods in Medical Image Processing
 IEEE Transactions on Medical Imaging
, 1999
"... Abstract — Image interpolation techniques often are required in medical imaging for image generation (e.g., discrete back projection for inverse Radon transform) and processing such as compression or resampling. Since the ideal interpolation function spatially is unlimited, several interpolation ker ..."
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Cited by 87 (1 self)
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Abstract — Image interpolation techniques often are required in medical imaging for image generation (e.g., discrete back projection for inverse Radon transform) and processing such as compression or resampling. Since the ideal interpolation function spatially is unlimited, several interpolation kernels of finite size have been introduced. This paper compares 1) truncated and windowed sinc; 2) nearest neighbor; 3) linear; 4) quadratic; 5) cubic Bspline; 6) cubic; g) Lagrange; and 7) Gaussian interpolation and approximation techniques with kernel sizes from 1 2 1upto 8 2 8. The comparison is done by: 1) spatial and Fourier analyses; 2) computational complexity as well as runtime evaluations; and 3) qualitative and quantitative interpolation error determinations for particular interpolation tasks which were taken from common situations in medical image processing. For local and Fourier analyses, a standardized notation is introduced
Quantitative Fourier Analysis of Approximation Techniques: Part II  Wavelets
 IEEE Trans. Signal Processing
, 1999
"... In a previous paper, we proposed a general Fourier method that provides an accurate prediction of the approximation error, irrespective of the scaling properties of the approximating functions. Here, we apply our results when these functions satisfy the usual twoscale relation encountered in dyadic ..."
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Cited by 63 (28 self)
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In a previous paper, we proposed a general Fourier method that provides an accurate prediction of the approximation error, irrespective of the scaling properties of the approximating functions. Here, we apply our results when these functions satisfy the usual twoscale relation encountered in dyadic multiresolution analysis. As a consequence of this additional constraint, the quantities introduced in our previous paper can be computed explicitly as a function of the refinement filter. This is, in particular, true for the asymptotic expansion of the approximation error for biorthonormal wavelets as the scale tends to zero. One of the contributions of this paper is the computation of sharp, asymptotically optimal upper bounds for the leastsquares approximation error. Another contribution is the application of these results to Bsplines and Daubechies scaling functions, which yields explicit asymptotic developments and upper bounds. Thanks to these explicit expressions, we can quantify ...
A chronology of interpolation: From ancient astronomy to modern signal and image processing
 Proceedings of the IEEE
, 2002
"... This paper presents a chronological overview of the developments in interpolation theory, from the earliest times to the present date. It brings out the connections between the results obtained in different ages, thereby putting the techniques currently used in signal and image processing into histo ..."
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Cited by 61 (0 self)
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This paper presents a chronological overview of the developments in interpolation theory, from the earliest times to the present date. It brings out the connections between the results obtained in different ages, thereby putting the techniques currently used in signal and image processing into historical perspective. A summary of the insights and recommendations that follow from relatively recent theoretical as well as experimental studies concludes the presentation. Keywords—Approximation, convolutionbased interpolation, history, image processing, polynomial interpolation, signal processing, splines. “It is an extremely useful thing to have knowledge of the true origins of memorable discoveries, especially those that have been found not by accident but by dint of meditation. It is not so much that thereby history may attribute to each man his own discoveries and others should be encouraged to earn like commendation, as that the art of making discoveries should be extended by considering noteworthy examples of it. ” 1 I.
Generalizations of the sampling theorem: Seven decades after Nyquist
 IEEE Trans. Circuits and Systems
, 2001
"... Abstract. 1 The sampling theorem is one of the most basic and fascinating topics in engineering sciences. The most well known form is Shannon’s uniform sampling theorem for bandlimited signals. Extensions of this to bandpass signals and multiband signals, and to nonuniform sampling are also wellkno ..."
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Cited by 37 (3 self)
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Abstract. 1 The sampling theorem is one of the most basic and fascinating topics in engineering sciences. The most well known form is Shannon’s uniform sampling theorem for bandlimited signals. Extensions of this to bandpass signals and multiband signals, and to nonuniform sampling are also wellknown. The connection between such extensions and the theory of filter banks in DSP has been well established. This paper presents some of the less known aspects of sampling, with special emphasis on non bandlimited signals, pointwise stability of reconstruction, and reconstruction from nonuniform samples. Applications in multiresolution computation and in digital spline interpolation are also reviewed.
Cardinal exponential splines: Part I—Theory and filtering algorithms
 IEEE Trans. Signal Process
, 2005
"... Abstract—Causal exponentials play a fundamental role in classical system theory. Starting from those elementary building blocks, we propose a complete and selfcontained signal processing formulation of exponential splines defined on a uniform grid. We specify the corresponding Bspline basis functi ..."
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Cited by 36 (13 self)
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Abstract—Causal exponentials play a fundamental role in classical system theory. Starting from those elementary building blocks, we propose a complete and selfcontained signal processing formulation of exponential splines defined on a uniform grid. We specify the corresponding Bspline basis functions and investigate their reproduction properties (Green function and exponential polynomials); we also characterize their stability (Riesz bounds). We show that the exponential Bspline framework allows an exact implementation of continuoustime signal processing operators including convolution, differential operators, and modulation, by simple processing in the discrete Bspline domain. We derive efficient filtering algorithms for multiresolution signal extrapolation and approximation, extending earlier results for polynomial splines. Finally, we present a new asymptotic error formula that predicts the magnitude and the thorder decay of the Papproximation error as a function of the knot spacing. Index Terms—Continuoustime signal processing, convolution, differential operators, Green functions, interpolation, modulation, multiresolution approximation, splines. I.