Browsing by Author "Crouse, Matthew"

Now showing 1 - 15 of 15
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    Contextual Hidden Markov Models for Wavelet-domain Signal Processing
    (1997-11-01) Crouse, Matthew; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
    Wavelet-domain hidden Markov models (HMMs) provide a powerful new approach for statistical modeling and processing of wavelet coefficients. In addition to characterizing the statistics of individual wavelet coefficients, HMMs capture some of the key interactions between wavelet coefficients. However, as HMMs model an increasing number of wavelet coefficient interactions, HMM-based signal processing becomes increasingly complicated. In this paper, we propose a new approach to HMMs based on the notion of context. By modeling wavelet coefficient inter-dependencies via contexts, we retain the approximation capabilities of HMMs, yet substantially reduce their complexity. To illustrate the power of this approach, we develop new algorithms for signal estimation and for efficient synthesis of nonGaussian, long-range-dependent network traffic.
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    Fast, Exact Synthesis of Gaussian and nonGaussian Long-Range-Dependent Processes
    (2009-04-15) Baraniuk, Richard; Crouse, Matthew
    1/f noise and statistically self-similar random processes such as fractional Brownian motion (fBm) and fractional Gaussian noise (fGn) are fundamental models for a host of real-world phenomena, from network traffic to DNA to the stock market. Synthesis algorithms play a key role by providing the feedstock of data necessary for running complex simulations and accurately evaluating analysis techniques. Unfortunately, current algorithms to correctly synthesize these long-range dependent (LRD) processes are either abstruse or prohibitively costly, which has spurred the wide use of inexact approximations. To fill the gap, we develop a simple, fast (O(N logN) operations for a length-N signal) framework for exactly synthesizing a range of Gaussian and nonGaussian LRD processes. As a bonus, we introduce and study a new bi-scaling fBm process featuring a "kinked" correlation function that exhibits distinct scaling laws at coarse and fine scales.
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    Fast, Exact Synthesis of Gaussian and nonGaussian Long-Range-Dependent Processes
    (1999-01-15) Crouse, Matthew; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
    1/f noise and statistically self-similar processes such as fractional Brownian motion (fBm) are vital for modeling numerous real-world phenomena, from network traffic to DNA to the stock market. Although several algorithms exist for synthesizing discrete-time samples of a 1/f process, these algorithms are inexact, meaning that the covariance of the synthesized processes can deviate significantly from that of a true 1/f process. However, the Fast Fourier Transform (FFT) can be used to exactly and efficiently synthesize such processes in O(N logN) operations for a length-N signal. Strangely enough, the key is to apply the FFT to match the target process's covariance structure, not its frequency spectrum. In this paper, we prove that this FFT-based synthesis is exact not only for 1/f processes such as fBm, but also for a wide class of long-range dependent processes. Leveraging the flexibility of the FFT approach, we develop new models for processes that exhibit one type of fBm scaling behavior over fine resolutions and a distinct scaling behavior over coarse resolutions. We also generalize the method in order to exactly synthesize various nonGaussian 1/f processes. Our nonGaussian 1/f synthesis is fast and simple. Used in simulations, our synthesis techniques could lead to new insights into areas such as computer networking, where the traffic processes exhibit nonGaussianity and a richer covariance than that of a strict fBm process.
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    Hidden Markov Models for Wavelet-based Signal Processing
    (1996-11-01) Crouse, Matthew; Baraniuk, Richard G.; Nowak, Robert David; Digital Signal Processing (http://dsp.rice.edu/)
    Current wavelet-based statistical signal and image processing techniques such as shrinkage and filtering treat the wavelet coefficients as though they were statistically independent. This assumption is unrealistic; considering the statistical dependencies between wavelet coefficients can yield substantial performance improvements. In this paper we develop a new framework for wavelet-based signal processing that employs hidden Markov models to characterize the dependencies between wavelet coefficients. To illustrate the power of the new framework, we derive a new signal denoising algorithm that outperforms current scalar shrinkage techniques.
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    Multifractal Signal Models with Application to Network Traffic
    (1998-08-01) Crouse, Matthew; Riedi, Rudolf H.; Ribeiro, Vinay Joseph; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
    In this paper, we develop a new multiscale modeling framework for characterizing positive-valued data with long-range-dependent 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 N-point data sets. We study both the second-order 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 (variance-time 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.
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    A Multifractal Wavelet Model for Positive Processes
    (1998-10-01) Crouse, Matthew; Riedi, Rudolf H.; Ribeiro, Vinay Joseph; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
    In this paper, we develop a new multiscale modeling framework for characterizing positive-valued data with long-range-dependent 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 N-point data sets. We study both the second-order 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 (variance-time 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.
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    A Multifractal Wavelet Model with Application to Network Traffic
    (1999-04-01) Riedi, Rudolf H.; Crouse, Matthew; Ribeiro, Vinay Joseph; Baraniuk, Richard G.; Center for Multimedia Communications (http://cmc.rice.edu/)
    In this paper, we develop a new multiscale modeling framework for characterizing positive-valued data with long-range-dependent 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 N-point data sets. We study both the second-order 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 (variance-time 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.
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    Multiscale Queuing Analysis of Long-Range-Dependent Network Traffic
    (2000-03-01) Ribeiro, Vinay Joseph; Riedi, Rudolf H.; Crouse, Matthew; Baraniuk, Richard G.; Center for Multimedia Communications (http://cmc.rice.edu/)
    Many studies have indicated the importance of capturing scaling properties when modeling traffic loads; however, the influence of long-range dependence (LRD) and marginal statistics still remains on unsure footing. In this paper, we study these two issues by introducing a multiscale traffic model and a novel multiscale approach to queuing analysis. The multifractal wavelet model (MWM) is a multiplicative, wavelet-based model that captures the positivity, LRD, and "spikiness" of non-Gaussian traffic. Using a binary tree, the model synthesizes an N-point data set with only O(N)computations. Leveraging the tree structure of the model, we derive a multiscale queuing analysis that provides a simple closed form approximation to the tail queue probability, valid for any given buffer size. The analysis is applicable not only to the MWM but to tree-based models in general, including fractional Gaussian noise. Simulated queuing experiments demonstrate the accuracy of the MWM for matching real data traces and the precision of our theoretical queuing formula. Thus, the MWM is useful not only for fast synthesis of data for simulation purposes but also for applications requiring accurate queuing formulas such as call admission control. Our results clearly indicate that the marginal distribution of traffic at different time-resolutions affects queuing and that a Gaussian assumption can lead to over-optimistic predictions of tail queue probability even when taking LRD into account.
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    Multiscale Queuing Analysis of Long-Range-Dependent Network Traffic
    (2001-02-20) Ribeiro, Vinay Joseph; Riedi, Rudolf H.; Crouse, Matthew; Baraniuk, Richard G.; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/)
    This paper develops a novel approach to queuing analysis tailor-made for multiscale long-range-dependent (LRD) traffic models. We review two such traffic models, the wavelet-domain independent Gaussian model (WIG) and the multifractal wavelet model (MWM). The WIG model is a recent generalization of the ubiquitous fractional Brownian motion process. Both models are based on a multiscale binary tree structure that captures the correlation structure of traffic and hence its LRD. Due to its additive nature, the WIG is inherently Gaussian, while the multiplicative MWM is non-Gaussian. The MWM is set within the framework of multifractals, which provide natural tools to measure the multiscale statistical properties of traffic loads, in particular their burstiness. Our queuing analysis leverages the tree structure of the models and provides a simple closed-form approximation to the tail queue probability for any given queue size. This makes the WIG and MWM suitable for numerous practical applications, including congestion control, admission control, and cross-traffic estimation. The queuing analysis reveals that the marginal distribution and, in particular, the large values of traffic at different time scales strongly affect queuing. This implies that merely modeling the traffic variance at multiple time scales, or equivalently, the second-order correlation structure, can be insufficient for capturing the queuing behavior of real traffic. We confirm these analytical findings by comparing the queuing behavior of WIG and MWM traffic through simulations.
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    Network Traffic Modeling using a Multifractal Wavelet Model
    (1999-02-01) Riedi, Rudolf H.; Crouse, Matthew; Ribeiro, Vinay Joseph; Baraniuk, Richard G.; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/)
    In this paper, we describe a new multiscale model for characterizing positive-valued and long-range dependent data. The model uses the Haar wavelet transform and puts a constraint on the wavelet coefficients to guarantee positivity, which results in a swift O(N) algorithm to synthesize N-point data sets. We elucidate our model's ability to capture the covariance structure of real data, study its multifractal properties, and derive a scheme for matching it to real data observations. We demonstrate the model's utility by applying it to network traffic synthesis. The flexibility and accuracy of the model and fitting procedure result in a close match to the real data statistics (variance-time plots) and queuing behavior.
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    Network Traffic Modeling using a Multifractal Wavelet Model
    (2000-07-01) Riedi, Rudolf H.; Ribeiro, Vinay Joseph; Crouse, Matthew; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
    In this paper, we develop a simple and powerful multiscale model for syntheizing nonFaussian, long-range dependent (LRD) network traffic. Although wavelets effectively decorrelate LRD data, wavelet-based models have generally been restricted by a Gaussianity assumption that can be un-realistic for traffic. Using a multiplicative superstructure on top of the Haar wavelet transform, we exploit the decorrelating properties of wavelets while simultaneously capturing the positivity and "spikiness" of nonGaussian traffic. This leads to a swift O(N) algorithm for fitting and synthesizing N-point data sets. The resulting model belongs to the class of multifractal cascades, a set of processes with rich statistical properties. We elucidate our model's ability to capture the covariance structure of real data and then fit it to real traffic traces. Queueing experiments demonstrate the accuracy of the model for matching real data.
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    Signal Estimation using Wavelet-Markov Models
    (1997-04-01) Crouse, Matthew; Baraniuk, Richard G.; Nowak, Robert David; Digital Signal Processing (http://dsp.rice.edu/)
    Current wavelet-based statistical signal and image processing techniques such as shrinkage and filtering treat the wavelet coefficients as though they were statistically independent. This assumption is unrealistic; considering the statistical dependencies between wavelet coefficients can yield substantial performance improvements. We develop a new framework for wavelet-based signal processing that employs hidden Markov models to characterize the dependencies between wavelet coefficients. To illustrate the power of the new framework, we derive a new algorithm for signal estimation in nonGaussian noise.
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    Simplified Wavelet-Domain Hidden Markov Models using Contexts
    (1998-05-01) Crouse, Matthew; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
    Wavelet-domain hidden Markov models (HMMs) are a potent new tool for modeling the statistical properties of wavelet transforms. In addition to characterizing the statistics of individual wavelet coefficients, HMMs capture the salient interactions between wavelet coefficients. However, as we model an increasing number of wavelet coefficient interactions, HMM-based signal processing becomes increasingly complicated. In this paper, we propose a new approach to HMMs based on the notion of context. By modeling wavelet coefficient inter-dependencies via contexts, we retain the approximation capabilities of HMMs, yet substantially reduce their complexity. To illustrate the power of this approach, we develop new algorithms for signal estimation and for efficient synthesis of nonGaussian, long-range-dependent network traffic.
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    Simulation of Non-Gaussian Long-Range-Dependent Traffic using Wavelets
    (1999-05-01) Ribeiro, Vinay Joseph; Riedi, Rudolf H.; Crouse, Matthew; Baraniuk, Richard G.; Center for Multimedia Communications (http://cmc.rice.edu/)
    In this paper, we develop a simple and powerful multiscale model for the synthesis of non-Gaussian, long-range dependent (LRD) network traffic. Although wavelets effectively decorrelate LRD data, wavelet-based models have generally been restricted by a Gaussianity assumption that can be unrealistic for traffic. Using a ultiplicative superstructure on top of the Haar wavelet transform, we exploit the decorrelating properties of wavelets while simultaneously capturing the positivity and "spikiness" of nonGaussian traffic. This leads to a swift O(N) algorithm for fitting and synthesizing N-point data sets. The resulting model belongs to the class of multifractal cascades, a set of processes with rich statistical properties. We elucidate our model's ability to capture the covariance structure of real data and then fit it to real traffic traces. Queueing experiments demonstrate the accuracy of the model for matching real data. Our results indicate that the nonGaussian nature of traffic has a significant effect on queuing.
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    Wavelet -Based Statistical Signal Processing using Hidden Markov Models
    (1998-04-01) Crouse, Matthew; Nowak, Robert David; Baraniuk, Richard G.; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/)
    Wavelet-based statistical signal processing techniques such as denoising and detection typically model the wavelet coefficients as independent or jointly Gaussian. These models are unrealistic for many real-world signals. In this paper, we develop a new framework for statistical signal processing based on wavelet-domain hidden Markov models (HMMs). The framework enables us to concisely model the statistical dependencies and non-Gaussian Statistics encountered with real-world signals. Wavelet-domain HMMs are designed with the intrinsic properties of the wavelet transform in mind and provide powerful yet tractable probabilistic signal modes. Efficient Expectation Maximization algorithms are developed for fitting the HMMs to observational signal data. The new framework is suitable for a wide range of applications, including signal estimation, detection, classification, prediction, and even synthesis. To demonstrate the utility of wavelet-domain HMMs, we develop novel algorithms for signal denoising, classificaion, and detection.