Matthew Crouse
Rice University
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Publication
Featured researches published by Matthew Crouse.
IEEE Transactions on Signal Processing | 1998
Matthew Crouse; Robert D. Nowak; Richard G. Baraniuk
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. We develop a new framework for statistical signal processing based on wavelet-domain hidden Markov models (HMMs) that concisely models the statistical dependencies and non-Gaussian statistics encountered in 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 models. 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, classification, and detection.
IEEE Transactions on Information Theory | 1999
Rudolf H. Riedi; Matthew Crouse; Vinay J. Ribeiro; Richard G. Baraniuk
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.
measurement and modeling of computer systems | 1999
Vinay J. Ribeiro; Rudolf H. Riedi; Matthew Crouse; Richard G. Baraniuk
In this paper, we develop a simple and powerful multiscale model for the synthesis of nonGaussian, 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 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. Our results indicate that the nonGaussian nature of traffic has a significant effect on queuing.
asilomar conference on signals, systems and computers | 1996
Matthew Crouse; Richard G. Baraniuk; Robert D. Nowak
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.
IEEE International Symposium on Digital Signal Processing for Communication Systems (DSPCS) | 2001
Rudolf H. Riedi; Vinay J. Ribeiro; Matthew Crouse; Richard G. Baraniuk
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 algorithm to synthesize -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 fle xibility and accuracy of the model and fitting procedure result in a close match to the real data statistics (variance-time plots) and queuing behavior.
international conference on acoustics speech and signal processing | 1998
Matthew Crouse; Richard G. Baraniuk
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.
international conference on acoustics, speech, and signal processing | 1997
Matthew Crouse; Richard G. Baraniuk; Robert D. Nowak
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.
Wavelet applications in signal and image processing. Conference | 1997
Matthew Crouse; Robert D. Nowak; Richard G. Baraniuk
Most wavelet-based statistical signal and image processing techniques 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.
conference on advanced signal processing algorithms architectures and implemenations | 1997
Matthew Crouse; Robert D. Nowak; K. Mhirsi; Richard G. Baraniuk
This paper addresses the problem of detection and classification of complicated signals in noise. Classical detection methods such as energy detectors and linear discriminant analysis do not perform well in many situations of practical interest. We introduce a new approach based on hidden Markov modeling in the wavelet domain. Using training data, we fit a hidden Markov model (HMM) to the wavelet transform to concisely represent its probabilistic time- frequency structure. The HMM provides a natural framework for performing likelihood ratio tests used in signal detection and classification. We compare our approach with classical methods for classification of nonlinear processes, change-point detection, and detection with unknown delay.
ieee sp international symposium on time frequency and time scale analysis | 1998
Matthew Crouse; Rudolf H. Riedi; Vinay J. Ribeiro; Richard G. Baraniuk
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 models 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 models 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 behaviour.