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39
Efficient multiscale regularization with applications to the computation of optical flow
 IEEE Trans. Image Process
, 1994
"... AbsfruetA new approach to regularization methods for image processing is introduced and developed using as a vehicle the problem of computing dense optical flow fields in an image sequence. Standard formulations of this problem require the computationally intensive solution of an elliptic partial d ..."
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Cited by 99 (33 self)
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AbsfruetA new approach to regularization methods for image processing is introduced and developed using as a vehicle the problem of computing dense optical flow fields in an image sequence. Standard formulations of this problem require the computationally intensive solution of an elliptic partial differential equation that arises from the often used “smoothness constraint” ’yl”. regularization. The interpretation of the smoothness constraint is utilized as a “fractal prior ” to motivate regularization based on a recently introduced class of multiscale stochastic models. The solution of the new problem formulation is computed with an efficient multiscale algorithm. Experiments on several image sequences demonstrate the substantial computational savings that can be achieved due to the fact that the algorithm is noniterative and in fact has a per pixel computational complexity that is independent of image size. The new approach also has a number of other important advantages. Specifically, multiresolution flow field estimates are available, allowing great flexibility in dealing with the tradeoff between resolution and accuracy. Multiscale error covariance information is also available, which is of considerable use in assessing the accuracy of the estimates. In particular, these error statistics can be used as the basis for a rational procedure for determining the spatiallyvarying optimal reconstruction resolution. Furthermore, if there are compelling reasons to insist upon a standard smoothness constraint, our algorithm provides an excellent initialization for the iterative algorithms associated with the smoothness constraint problem formulation. Finally, the usefulness of our approach should extend to a wide variety of illposed inverse problems in which variational techniques seeking a “smooth ” solution are generally Used. I.
Localization via ultrawideband radios
 IEEE Signal Processing Magazine
, 2005
"... A look at positioning aspects of future sensor networks. ..."
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Cited by 40 (5 self)
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A look at positioning aspects of future sensor networks.
Digital Audio Restoration
 Applications of Digital Signal Processing to Audio and Acoustics
, 1997
"... This chapter is concerned with the application of modern signal processing techniques to the restoration of degraded audio signals. Although attention is focussed on gramophone recordings, film sound tracks and tape recordings, many of the techniques discussed have applications in other areas where ..."
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Cited by 31 (11 self)
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This chapter is concerned with the application of modern signal processing techniques to the restoration of degraded audio signals. Although attention is focussed on gramophone recordings, film sound tracks and tape recordings, many of the techniques discussed have applications in other areas where degraded audio signals occur, such as speech transmission, telephony and hearing aids. We aim to provide a wide coverage of existing methodology while giving insight into current areas of research and future trends. 1 Introduction The introduction of high quality digital audio media such as Compact Disk (CD) and Digital Audio Tape (DAT) has dramatically raised general awareness and expectations about sound quality in all types of recordings. This, combined with an upsurge in interest in historical and nostalgic material, has led to a growing requirement for restoration of degraded sources ranging from the earliest recordings made on wax cylinders in the nineteenth century, through disc reco...
Image Processing with Multiscale Stochastic Models
, 1993
"... In this thesis, we develop image processing algorithms and applications for a particular class of multiscale stochastic models. First, we provide background on the model class, including a discussion of its relationship to wavelet transforms and the details of a twosweep algorithm for estimation. A ..."
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Cited by 30 (3 self)
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In this thesis, we develop image processing algorithms and applications for a particular class of multiscale stochastic models. First, we provide background on the model class, including a discussion of its relationship to wavelet transforms and the details of a twosweep algorithm for estimation. A multiscale model for the error process associated with this algorithm is derived. Next, we illustrate how the multiscale models can be used in the context of regularizing illposed inverse problems and demonstrate the substantial computational savings that such an approach offers. Several novel features of the approach are developed including a technique for choosing the optimal resolution at which to recover the object of interest. Next, we show that this class of models contains other widely used classes of statistical models including 1D Markov processes and 2D Markov random fields, and we propose a class of multiscale models for approximately representing Gaussian Markov random fields...
ON SOLVING ELLIPTIC STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
"... A model elliptic boundary value problem of second order, with stochastic coefficients described by the Karhunen–Loève expansion is addressed. This problem is transformed into an equivalent deterministic one. The perturbation method and the method of successive approximations is analyzed. Rigorous er ..."
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Cited by 13 (0 self)
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A model elliptic boundary value problem of second order, with stochastic coefficients described by the Karhunen–Loève expansion is addressed. This problem is transformed into an equivalent deterministic one. The perturbation method and the method of successive approximations is analyzed. Rigorous error estimates in the framework of Sobolev spaces are given.
Asymptotics in Quantum Statistics
 Institute of Mathematical Statistics
, 2001
"... This paper gives an introduction to this field in the most simple of settings, that of estimating the state of a spinhalf particle given n independent copies of the particle. We show how in some cases asymptotically optimal measurements can be constructed. Other cases present interesting open probl ..."
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Cited by 9 (7 self)
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This paper gives an introduction to this field in the most simple of settings, that of estimating the state of a spinhalf particle given n independent copies of the particle. We show how in some cases asymptotically optimal measurements can be constructed. Other cases present interesting open problems, connected to the fact that for some models, quantum Fisher information is in some sense nonadditive. In physical terms, we have nonlocality without entanglement. Keywords and phrases: Quantum statistics, information, spin half. AMS subject classifications: ??, ??. 1 Introduction
Asymptotically Minimax Nonparametric Regression in L2
 in L 2 . Statistics
, 1996
"... Introduction In the nonparametric regression context, the notion of asymptotic optimality usually associates with the "optimal rate of convergence". Minimax rates of convergence have been extensively studied (Ibragimov and Hasminskii (1980), (1982); Stone (1980), (1982) and many others). ..."
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Cited by 9 (0 self)
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Introduction In the nonparametric regression context, the notion of asymptotic optimality usually associates with the "optimal rate of convergence". Minimax rates of convergence have been extensively studied (Ibragimov and Hasminskii (1980), (1982); Stone (1980), (1982) and many others). Different estimators turn out to be optimal in the sense of the best rate of convergence. We mention only some of them: kernel estimators (Ibragimov and Hasminskii (1980), Korostelev (1993)), projection estimators (Ibragimov and Hasminskii (1981)), spline estimators (Speckman (1985), Nussbaum (1985)), wavelets (Donoho and Johnstone (1992)). From the practical point of view stochastic approximation estimators considered in Belitser and Korostelev (1992) are also of interest. However, comparing estimators on the basis of their rates of convergence does not make it possible to distinguish among estimators optimal in that sence. Also from a more practical point of view, such approach does not give
Extended MLSE diversity receiver for the time and frequency selective channel
 IEEE Trans. on Communications
, 1997
"... ..."
Waveletpacketbased multiple access communication
 Willsky AS & Karl WC
, 1994
"... Optimal joint detection for interfering (nonorthogonal) users in a multiple access communication system has, in general, a computational complexity which is exponential in the number of users. For this reason, optimal joint detection has been thought impractical for large numbers of users. A number ..."
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Cited by 5 (1 self)
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Optimal joint detection for interfering (nonorthogonal) users in a multiple access communication system has, in general, a computational complexity which is exponential in the number of users. For this reason, optimal joint detection has been thought impractical for large numbers of users. A number of suboptimal low complexity joint detectors have been proposed for direct sequence spread spectrum user waveforms which have properties suitable for mobile cellular systems. There are, however, other systems, such as satellite systems, for which other waveforms may be considered. This thesis shows that there are user signature set selections which enable optimal joint detection that is extremely low in complexity. When a hierarchical crosscorrelation structure is imposed on the user waveforms, optimal detection can be achieved with a treestructured receiver having complexity that is, in typical cases, a loworderpolynomial in the number of users. This is a huge savings over the exponential complexity needed for the optimal detection of general signals. Work in recent literature has shown that a hierarchically structured signal set
On Minimax Filtering over Ellipsoids
 Math. Meth. Statist
, 1995
"... this article, developing further the approach of [9], we describe the secondorder behaviour of the minimax estimators and the quadratic minimax risk for the model (1) (2). These results are illustrated by a number of examples. The authors are grateful to G.K. Golubev for a number of comments resu ..."
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Cited by 5 (2 self)
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this article, developing further the approach of [9], we describe the secondorder behaviour of the minimax estimators and the quadratic minimax risk for the model (1) (2). These results are illustrated by a number of examples. The authors are grateful to G.K. Golubev for a number of comments resulting in the improvement of some results of the paper and their better presentation. 2 Minimax linear estimation