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Waveletbased statistical signal processing using hidden Markov models
 IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 1998
"... Waveletbased 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 realworld 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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Waveletbased 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 realworld signals. In this paper, we develop a new framework for statistical signal processing based on waveletdomain hidden Markov models (HMM’s) that concisely models the statistical dependencies and nonGaussian statistics encountered in realworld signals. Waveletdomain 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 waveletdomain HMM’s, we develop novel algorithms for signal denoising, classification, and detection.
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.
Multiscale Image Segmentation using WaveletDomain Hidden Markov Models
 IEEE Trans. Image Processing
, 1999
"... We introduce a new image texture segmentation algorithm, HMTseg, based on wavelets and the hidden Markov tree (HMT) model. The HMT is a treestructured probabilistic graph that captures the statistical properties of the coefficients of the wavelet transform. Since the HMT is particularly well suited ..."
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Cited by 106 (6 self)
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We introduce a new image texture segmentation algorithm, HMTseg, based on wavelets and the hidden Markov tree (HMT) model. The HMT is a treestructured probabilistic graph that captures the statistical properties of the coefficients of the wavelet transform. Since the HMT is particularly well suited to images containing singularities (edges and ridges), it provides a good classifier for distinguishing between textures. Utilizing the inherent tree structure of the wavelet HMT and its fast training and likelihood computation algorithms, we perform multiscale texture classification at a range of different scales. We then fuse these multiscale classifications using a Bayesian probabilistic graph to obtain reliable final segmentations. Since HMTseg works on the wavelet transform of the image, it can directly segment waveletcompressed images without the need for decompression into the space domain. We demonstrate the performance of HMTseg with synthetic, aerial photo, and document image seg...
Multiscale autoregressive models and wavelets
, 1999
"... The multiscale autoregressive (MAR) framework was introduced to support the development of optimal multiscale statistical signal processing. Its power resides in the fast and flexible algorithms to which it leads. While the MAR framework was originally motivated by wavelets, the link between these t ..."
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Cited by 26 (4 self)
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The multiscale autoregressive (MAR) framework was introduced to support the development of optimal multiscale statistical signal processing. Its power resides in the fast and flexible algorithms to which it leads. While the MAR framework was originally motivated by wavelets, the link between these two worlds has been previously established only in the simple case of the Haar wavelet. The first contribution of this paper is to provide a unification of the MAR framework and all compactly supported wavelets as well as a new view of the multiscale stochastic realization problem. The second contribution of this paper is to develop waveletbased approximate internal MAR models for stochastic processes. This will be done by incorporating a powerful synthesis algorithm for the detail coefficients which complements the usual wavelet reconstruction algorithm for the scaling coefficients. Taking advantage of the statistical machinery provided by the MAR framework, we will illustrate the application of our models to samplepath generation and estimation from noisy, irregular, and sparse measurements.
Image Segmentation using Waveletdomain Classification
 in Proceedings of SPIE technical conference on Mathematical Modeling, Bayesian Estimation, and Inverse Problems
, 1999
"... We introduce a new image texture segmentation algorithm, HMTseg, based on waveletdomain hidden Markov tree (HMT) models. The HMT model is a treestructured probabilistic graph that captures the statistical properties of wavelet coefficients. Since the HMT is particularly well suited to images conta ..."
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Cited by 20 (4 self)
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We introduce a new image texture segmentation algorithm, HMTseg, based on waveletdomain hidden Markov tree (HMT) models. The HMT model is a treestructured probabilistic graph that captures the statistical properties of wavelet coefficients. Since the HMT is particularly well suited to images containing singularities (edges and ridges), it provides provides a good classifier for textures. Utilizing the inherent tree structure of the wavelet HMT and its fast training and likelihood computation algorithms, we perform multiscale texture classification at various scales. We then fuse these multiscale classifications using a Bayesian probabilistic graph to obtain a reliable final segmentation. Since HMTseg works on the wavelet transform of the image, it can directly segment waveletcompressed images, without the need for decompression. We demonstrate the performance of HMTseg with synthetic, aerial photo, and document image segmentations. 1. INTRODUCTION 1.1. Image Segmentation The image...
Multiscale SAR image segmentation using waveletdomain hidden Markov tree models. Pages 110 120 of
 Proceedings of the SPIE lJth International Symposium on Aerospace/Defense Sensing, Simulation, and Controls, Algorithms for Synthetic Aperture Radar Imagery VII
, 2000
"... We study the segmentation of SAR imagery using waveletdomain Hidden Markov Tree (HMT) models. The HMT model is a treestructured probabilistic graph that captures the statistical properties of the wavelet transforms of images. This technique has been successfully applied to the segmentation of natu ..."
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Cited by 5 (1 self)
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We study the segmentation of SAR imagery using waveletdomain Hidden Markov Tree (HMT) models. The HMT model is a treestructured probabilistic graph that captures the statistical properties of the wavelet transforms of images. This technique has been successfully applied to the segmentation of natural texture images, documents, etc. However, SAR image segmentation poses a di cult challenge owing to the high levels of speckle noise present at ne scales. We solve this problem using a \truncated &quot; wavelet HMT model specially adapted to SAR images. This variation is built using only the coarse scale wavelet coe cients. When applied to SAR images, this technique provides a reliable initial segmentation. We then re ne the classi cation using a multiscale fusion technique, which combines the classi cation information across scales from the initial segmentation to correct for misclassi cations. We provide a fast algorithm, and demonstrate its performance on MSTAR clutter data.
Multiscale Document Segmentation using WaveletDomain Hidden Markov Models
 in Proc. of IST/SPIE's 12th Annual Symp.  Electronic Imaging 2000
, 2000
"... We introduce a new document image segmentation algorithm, HMTseg, based on wavelets and the hidden Markov tree (HMT) model. The HMT is a treestructured probabilistic graph that captures the statistical properties of the coefficients of the wavelet transform. Since the HMT is particularly well suite ..."
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Cited by 5 (1 self)
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We introduce a new document image segmentation algorithm, HMTseg, based on wavelets and the hidden Markov tree (HMT) model. The HMT is a treestructured probabilistic graph that captures the statistical properties of the coefficients of the wavelet transform. Since the HMT is particularly well suited to images containing singularities (edges and ridges), it provides a good classifier for distinguishing between different document textures. Utilizing the inherent tree structure of the wavelet HMT and its fast training and likelihood computation algorithms, we perform multiscale texture classification at a range of different scales. We then fuse these multiscale classifications using a Bayesian probabilistic graph to obtain reliable final segmentations. Since HMTseg works on the wavelet transform of the image, it can directly segment waveletcompressed images, without the need for decompression into the space domain. We demonstrate HMTseg's performance with both synthetic and real imagery....
Multiscale Discriminant Saliency for Visual Attention
"... Abstract. The bottomup saliency, an early stage of humans ’ visual attention, can be considered as a binary classification problem between center and surround classes. Discriminant power of features for the classification is measured as mutual information between features and two classes distribut ..."
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Abstract. The bottomup saliency, an early stage of humans ’ visual attention, can be considered as a binary classification problem between center and surround classes. Discriminant power of features for the classification is measured as mutual information between features and two classes distribution. The estimated discrepancy of two feature classes very much depends on considered scale levels; then, multiscale structure and discriminant power are integrated by employing discrete wavelet features and Hidden markov tree (HMT). With wavelet coefficients and Hidden Markov Tree parameters, quadtree like label structures are constructed and utilized in maximum a posterior probability (MAP) of hidden class variables at corresponding dyadic subsquares. Then, saliency value for each dyadic square at each scale level is computed with discriminant power principle and the MAP. Finally, across multiple scales is integrated the final saliency map by an information maximization rule. Both standard quantitative tools such as NSS, LCC, AUC and qualitative assessments are used for evaluating the proposed multiscale discriminant saliency method (MDIS) against the wellknow informationbased saliency method AIM on its Bruce Database wity eyetracking data. Simulation results are presented and analyzed to verify the validity of MDIS as well as point out its disadvantages for further research direction.
Multiscale Discriminant Saliency with Waveletbased Hidden Markov Tree Modelling
"... Bottomup saliency, an early stage of human visual attention, can be considered as a binary classification problem between centre and surround classes. Discriminant power of features for the classification is measured as mutual information between distributions of image features and corresponding ..."
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Bottomup saliency, an early stage of human visual attention, can be considered as a binary classification problem between centre and surround classes. Discriminant power of features for the classification is measured as mutual information between distributions of image features and corresponding classes. As the estimated discrepancy very much depends on considered scale level, multiscale structure and discriminant power are integrated by employing discrete wavelet features and Hidden Markov Tree (HMT). With wavelet coefficients and Hidden Markov Tree parameters, quadtree like label structures are constructed and utilized in maximum a posterior probability (MAP) of hidden class variables at corresponding dyadic subsquares. A saliency value for each square block at each scale level is computed with discriminant power principle. Finally, across multiple scales is integrated the final saliency map by an information maximization rule. Both standard quantitative tools such as NSS, LCC, AUC and qualitative assessments are used for evaluating the proposed multiscale discriminant saliency (MDIS) against the wellknow information based approach AIM on its released image collection with eyetracking data. Simulation results are presented and analysed to verify the validity of MDIS as well as point out its limitation for further research direction. Preprint submitted to Elsevier February 1, 2013 ar X iv
WaveletBased Statistical Signal Processing Using Hidden Markov Models
, 2001
"... Estimation of bivariate measurements having different change points, with application to cognitive aging ..."
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Estimation of bivariate measurements having different change points, with application to cognitive aging