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603
Sampling signals with finite rate of innovation
 IEEE Transactions on Signal Processing
, 2002
"... Abstract—Consider classes of signals that have a finite number of degrees of freedom per unit of time and call this number the rate of innovation. Examples of signals with a finite rate of innovation include streams of Diracs (e.g., the Poisson process), nonuniform splines, and piecewise polynomials ..."
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Cited by 348 (69 self)
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Abstract—Consider classes of signals that have a finite number of degrees of freedom per unit of time and call this number the rate of innovation. Examples of signals with a finite rate of innovation include streams of Diracs (e.g., the Poisson process), nonuniform splines, and piecewise polynomials. Even though these signals are not bandlimited, we show that they can be sampled uniformly at (or above) the rate of innovation using an appropriate kernel and then be perfectly reconstructed. Thus, we prove sampling theorems for classes of signals and kernels that generalize the classic “bandlimited and sinc kernel ” case. In particular, we show how to sample and reconstruct periodic and finitelength streams of Diracs, nonuniform splines, and piecewise polynomials using sinc and Gaussian kernels. For infinitelength signals with finite local rate of innovation, we show local sampling and reconstruction based on spline kernels. The key in all constructions is to identify the innovative part of a signal (e.g., time instants and weights of Diracs) using an annihilating or locator filter: a device well known in spectral analysis and errorcorrection coding. This leads to standard computational procedures for solving the sampling problem, which we show through experimental results. Applications of these new sampling results can be found in signal processing, communications systems, and biological systems. Index Terms—Analogtodigital conversion, annihilating filters, generalized sampling, nonbandlimited signals, nonuniform splines, piecewise polynomials, poisson processes, sampling. I.
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 340 (27 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,
A wireless sensor network for structural monitoring
 SENSYS ’04: PROCEEDINGS OF THE 2ND INTERNATIONAL
, 2004
"... Structural monitoring—the collection and analysis of structural response to ambient or forced excitation–is an important application of networked embedded sensing with significant commercial potential. The first generation of sensor networks for structural monitoring are likely to be data acquisitio ..."
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Cited by 333 (12 self)
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Structural monitoring—the collection and analysis of structural response to ambient or forced excitation–is an important application of networked embedded sensing with significant commercial potential. The first generation of sensor networks for structural monitoring are likely to be data acquisition systems that collect data at a single node for centralized processing. In this paper, we discuss the design and evaluation of a wireless sensor network system (called Wisden) for structural data acquisition. Wisden incorporates two novel mechanisms, reliable data transport using a hybrid of endtoend and hopbyhop recovery, and lowoverhead data timestamping that does not require global clock synchronization. We also study the applicability of waveletbased compression techniques to overcome the bandwidth limitations imposed by lowpower wireless radios. We describe our implementation of these mechanisms on the Mica2 motes and evaluate the performance of our implementation. We also report experiences from deploying Wisden on a large structure.
Ratedistortion methods for image and video compression
 IEEE Signal Process. Mag. 1998
"... In this paper we provide an overview of ratedistortion (RD) based optimization techniques and their practical application to image and video coding. We begin with a short discussion of classical ratedistortion theory and then we show how in many practical coding scenarios, such as in standardsco ..."
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Cited by 222 (7 self)
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In this paper we provide an overview of ratedistortion (RD) based optimization techniques and their practical application to image and video coding. We begin with a short discussion of classical ratedistortion theory and then we show how in many practical coding scenarios, such as in standardscompliant coding environments, resource allocation can be put in an RD framework. We then introduce two popular techniques for resource allocation, namely, Lagrangian optimization and dynamic programming. After a discussion of these two techniques as well as some of their extensions, we conclude with a quick review of recent literature in these areas citing a number of applications related to image and video compression and transmission. We
A multifractal wavelet model with application to TCP network traffic
 IEEE TRANS. INFORM. THEORY
, 1999
"... In this paper, we develop a new multiscale modeling framework for characterizing positivevalued data with longrangedependent correlations (1=f noise). Using the Haar wavelet transform and a special multiplicative structure on the wavelet and scaling coefficients to ensure positive results, the mo ..."
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Cited by 213 (34 self)
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In this paper, we develop a new multiscale modeling framework for characterizing positivevalued data with longrangedependent correlations (1=f noise). Using the Haar wavelet transform and a special multiplicative structure on the wavelet and scaling coefficients to ensure positive results, the model provides a rapid O(N) cascade algorithm for synthesizing Npoint data sets. We study both the secondorder and multifractal properties of the model, the latter after a tutorial overview of multifractal analysis. We derive a scheme for matching the model to real data observations and, to demonstrate its effectiveness, apply the model to network traffic synthesis. The flexibility and accuracy of the model and fitting procedure result in a close fit to the real data statistics (variancetime plots and moment scaling) and queuing behavior. Although for illustrative purposes we focus on applications in network traffic modeling, the multifractal wavelet model could be useful in a number of other areas involving positive data, including image processing, finance, and geophysics.
Bayesian TreeStructured Image Modeling using Waveletdomain Hidden Markov Models
 IEEE Trans. Image Processing
, 1999
"... Waveletdomain hidden Markov models have proven to be useful tools for statistical signal and image processing. The hidden Markov tree (HMT) model captures the key features of the joint probability density of the wavelet coefficients of realworld data. One potential drawback to the HMT framework ..."
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Cited by 187 (17 self)
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Waveletdomain hidden Markov models have proven to be useful tools for statistical signal and image processing. The hidden Markov tree (HMT) model captures the key features of the joint probability density of the wavelet coefficients of realworld data. One potential drawback to the HMT framework is the need for computationally expensive iterative training to fit an HMT model to a given data set (using the ExpectationMaximization algorithm, for example). In this paper, we greatly simplify the HMT model by exploiting the inherent selfsimilarity of realworld images. This simplified model specifies the HMT parameters with just nine metaparameters (independent of the size of the image and the number of wavelet scales). We also introduce a Bayesian universal HMT (uHMT) that fixes these nine parameters. The uHMT requires no training of any kind. While extremely simple, we show using a series of image estimation /denoising experiments that these two new models retain nearly all of the key structure modeled by the full HMT. Finally, we propose a fast shiftinvariant HMT estimation algorithm that outperforms other waveletbased estimators in the current literature, both in meansquare error and visual metrics.
DIMENSIONS: Why do we need a new Data Handling architecture for Sensor Networks?
, 2002
"... An important class of networked systems is emerging that involve very large numbers of small, lowpower, wireless devices. These systems offer the ability to sense the environment densely, offering unprecedented opportunities for many scientific disciplines to obtain detailed datasets for analysis. ..."
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Cited by 167 (13 self)
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An important class of networked systems is emerging that involve very large numbers of small, lowpower, wireless devices. These systems offer the ability to sense the environment densely, offering unprecedented opportunities for many scientific disciplines to obtain detailed datasets for analysis. In this paper, we argue that a data handling architecture for these devices should incorporate their extreme resource constraints  energy, storage and processing  and spatiotemporal interpretation of the physical world in the design, cost model, and metrics of evaluation. We describe DIMENSIONS, a system that provides a unified view of data handling in sensor networks, incorporating longterm storage, multiresolution data access and spatiotemporal pattern mining.
LowComplexity Video Coding for ReceiverDriven Layered Multicast
 IEEE Journal on Selected Areas in Communications
, 1997
"... In recent years, the "Internet Multicast Backbone," or MBone, has risen from a small, research curiosity to a largescale and widely used communications infrastructure. A driving force behind this growth was the development of multipoint audio, video, and shared whiteboard conferencing appl ..."
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Cited by 164 (4 self)
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In recent years, the "Internet Multicast Backbone," or MBone, has risen from a small, research curiosity to a largescale and widely used communications infrastructure. A driving force behind this growth was the development of multipoint audio, video, and shared whiteboard conferencing applications. Because these realtime media are transmitted at a uniform rate to all of the receivers in the network, a source must either run at the bottleneck rate or overload portions of its multicast distribution tree. We overcome this limitation by moving the burden of rate adaptation from the source to the receivers with a scheme we call receiverdriven layered multicast, or RLM. In RLM, a source distributes a hierarchical signal by striping the different layers across multiple multicast groups, and receivers adjust their reception rate by simply joining and leaving multicast groups. In this paper, we describe a layered video compression algorithm which, when combined with RLM, provides a comprehensive solution for scalable multicast video transmission in heterogeneous networks. In addition to a layered representation, our coder has low complexity (admitting an efficient software implementation) and high loss resilience (admitting robust operation in loosely controlled environments like the Internet) . Even with these constraints, our hybrid DCT/waveletbased coder exhibits good compression performance. It outperforms all publicly available Internet video codecs while maintaining comparable runtime performance. We have implemented our coder in a "real" applicationthe UCB/LBL videoconferencing tool vic. Unlike previous work on layered video compression and transmission, we have built a fully operational system that is currently being deployed on a very large scale over the MBone.