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20
Wavelet-based statistical signal processing using hidden Markov models
- IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 1998
"... 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 b ..."
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Cited by 417 (55 self)
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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 (HMM’s) that concisely models the statistical dependencies and non-Gaussian statistics encountered in real-world signals. Wavelet-domain HMM’s 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 HMM’s 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 HMM’s, we develop novel algorithms for signal denoising, classification, and detection.
Bayesian Tree-Structured Image Modeling using Wavelet-domain Hidden Markov Models
- IEEE Trans. Image Processing
, 1999
"... Wavelet-domain 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 real-world data. One potential drawback to the HMT framework ..."
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Cited by 187 (17 self)
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Wavelet-domain 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 real-world 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 Expectation-Maximization algorithm, for example). In this paper, we greatly simplify the HMT model by exploiting the inherent self-similarity of real-world 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 shift-invariant HMT estimation algorithm that outperforms other wavelet-based estimators in the current literature, both in mean-square error and visual metrics.
Multiresolution markov models for signal and image processing
- Proceedings of the IEEE
, 2002
"... This paper reviews a significant component of the rich field of statistical multiresolution (MR) modeling and processing. These MR methods have found application and permeated the literature of a widely scattered set of disciplines, and one of our principal objectives is to present a single, coheren ..."
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Cited by 154 (19 self)
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This paper reviews a significant component of the rich field of statistical multiresolution (MR) modeling and processing. These MR methods have found application and permeated the literature of a widely scattered set of disciplines, and one of our principal objectives is to present a single, coherent picture of this framework. A second goal is to describe how this topic fits into the even larger field of MR methods and concepts–in particular making ties to topics such as wavelets and multigrid methods. A third is to provide several alternate viewpoints for this body of work, as the methods and concepts we describe intersect with a number of other fields. The principle focus of our presentation is the class of MR Markov processes defined on pyramidally organized trees. The attractiveness of these models stems from both the very efficient algorithms they admit and their expressive power and broad applicability. We show how a variety of methods and models relate to this framework including models for self-similar and 1/f processes. We also illustrate how these methods have been used in practice. We discuss the construction of MR models on trees and show how questions that arise in this context make contact with wavelets, state space modeling of time series, system and parameter identification, and hidden
Multiscale Bayesian Segmentation Using a Trainable Context Model
- IEEE Trans. on Image Processing
, 2001
"... In recent years, multiscale Bayesian approaches have attracted increasing attention for use in image segmentation. Generally, these methods tend to offer improved segmentation accuracy with reduced computational burden. Existing Bayesian segmentation methods use simple models of context designed to ..."
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Cited by 61 (1 self)
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In recent years, multiscale Bayesian approaches have attracted increasing attention for use in image segmentation. Generally, these methods tend to offer improved segmentation accuracy with reduced computational burden. Existing Bayesian segmentation methods use simple models of context designed to encourage large uniformly classified regions. Consequently, these context models have a limited ability to capture the complex contextual dependencies that are important in applications such as document segmentation. In this paper, we propose a multiscale...
Image modeling with position-encoding dynamic trees
- IEEE Trans. Pattern Anal. Machine Intell
, 2003
"... Abstract This paper describes the Position-Encoding Dynamic Tree (PEDT). The PEDT is a probabilistic model for images which improves on the Dynamic Tree by allowing the positions of objects to play a part in the model. This increases the flexibility of the model over the Dynamic Tree and allows the ..."
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Cited by 37 (0 self)
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Abstract This paper describes the Position-Encoding Dynamic Tree (PEDT). The PEDT is a probabilistic model for images which improves on the Dynamic Tree by allowing the positions of objects to play a part in the model. This increases the flexibility of the model over the Dynamic Tree and allows the positions of objects to be located and manipulated. The paper motivates and defines this form of probabilistic model using the belief network formalism. A structured variational approach for inference and learning in the PEDT is developed, and the resulting variational updates are obtained, along with additional implementation considerations which ensure the computational cost scales linearly in the number of nodes of the belief network. The PEDT model is demonstrated and compared with the dynamic tree and fixed tree. The structured variational learning method is compared with mean field approaches.
Quantitative analysis of the Drosophila segmentation regulatory network using pattern generating potentials
, 2010
"... Cis-regulatory modules that drive precise spatial-temporal patterns of gene expression are central to the process of metazoan development. We describe a new computational strategy to annotate genomic sequences based on their ‘‘pattern generating potential’ ’ and to produce quantitative descriptions ..."
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Cited by 21 (12 self)
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Cis-regulatory modules that drive precise spatial-temporal patterns of gene expression are central to the process of metazoan development. We describe a new computational strategy to annotate genomic sequences based on their ‘‘pattern generating potential’ ’ and to produce quantitative descriptions of transcriptional regulatory networks at the level of individual protein-module interactions. We use this approach to convert the qualitative understanding of interactions that regulate Drosophila segmentation into a network model in which a confidence value is associated with each transcription factor-module interaction. Sequence information from multiple Drosophila species is integrated with transcription factor binding specificities to determine conserved binding site frequencies across the genome. These binding site profiles are combined with transcription factor expression information to create a model to predict module activity patterns. This model is used to scan genomic sequences for the potential to generate all or part of the expression pattern of
IEEE SIGNAL PROCESSING LETTERS, SUBMITTED 1 Fast Approximation of Kullback-Leibler Distance for Dependence Trees and Hidden Markov Models
"... Abstract — We present a fast algorithm to approximate the Kullback-Leibler distance (KLD) between two dependence tree models. The algorithm uses the “upward ” (or “forward”) procedure to compute an upper bound for the KLD. For hidden Markov models, this algorithm is reduced to a simple expression. N ..."
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Abstract — We present a fast algorithm to approximate the Kullback-Leibler distance (KLD) between two dependence tree models. The algorithm uses the “upward ” (or “forward”) procedure to compute an upper bound for the KLD. For hidden Markov models, this algorithm is reduced to a simple expression. Numerical experiments show that for a similar accuracy, the proposed algorithm offers a saving of hundreds of times in computational complexity compared to the commonly used Monte-Carlo method. This makes the proposed algorithm important for real-time applications, like image retrieval. Keywords — Kullback-Leibler distance, models, hidden Markov models
TABLE OF CONTENTS
, 1999
"... To my beloved wife Liu, Qian. To my wonderful parents Cheng, Zuoqin and Li, Heying.- iii-ACKNOWLEDGMENTS I would like to extend my most sincere thanks to my advisor, Professor Charles A. Bouman for his guidance, encouragement and all the things that he had done in helping me develop my professional ..."
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To my beloved wife Liu, Qian. To my wonderful parents Cheng, Zuoqin and Li, Heying.- iii-ACKNOWLEDGMENTS I would like to extend my most sincere thanks to my advisor, Professor Charles A. Bouman for his guidance, encouragement and all the things that he had done in helping me develop my professional and personal skills. I am certain that I will benefit from his rigorous scientific approach, and the way of critical thinking throughout my future career. Most of all, my deepest thanks go to my wife Qian, my parents and my family. I can not thank them enough for their love, support, sacrifice and their belief in me. I want to thank my advisory committee members: Professor Jan P. Allebach, Professor Edward J. Delp, and Professor Bradley J. Lucier for their constructive suggestions and comments. Also, my thanks go to Dr. Zhigang Fan, Dr. Ricardo L. de Queiroz, Dr. Chi-hsin Wu and Dr. Steve J. Harrington of Xerox Corporation for their valuable advice and suggestions. I thank Dr. Faouzi Kossentini and Mr.
Digital Repository @ Iowa State University
, 2010
"... Hidden Markov models for simultaneous testing of multiple gene sets and adaptive and dynamic adaptive procedures for false discovery rate control and estimation ..."
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Hidden Markov models for simultaneous testing of multiple gene sets and adaptive and dynamic adaptive procedures for false discovery rate control and estimation
