Markov Tree Model Research Articles

SAR image segmentation algorithm based on Contourlet domain AFMRF model

Combining the advantage of Contourlet transform with adaptive fuzzy Markov random field (MRF) model, a novel segmentation algorithm is proposed in this study to achieve precise and continuous division for synthetic aperture radar (SAR) image. The classical MRF model is modified to obtain the edge and process adaptive label factor. The adaptive fuzzy MRF (AFMRF) model is proposed to equilibrate the smooth regions segmentation with texture regions segmentation. At the same time, Contourlet domain hidden Markov tree (HMT) model is introduced to perform multi-scale directional filtering and intra-scale training on the coefficients of SAR images to achieve precise texture segmentation at each scale. Finally, the AFMRF model is integrated into inter-scale and intra-scale HMT training results and the segmented image can be obtained. To verify the validity of the proposed algorithm, several SAR images are experimented and compared with the state-of-the-art algorithms. The experimental results and analysis show that the proposed algorithm can achieve better results on noise suppression, smoothness of target regions, precise and continuous segmentation of fuzzy texture.

Quantum correlations for a simple kicked system with mixed phase space.

We investigate both the classical and quantum dynamics for a simple kicked system (the standard map) that classically has mixed phase space. For initial conditions in a portion of the chaotic region that is close enough to the regular region, the phenomenon of sticking leads to a power-law decay with time of the classical correlation function of a simple observable. Quantum mechanically, we find the same behavior, but with a smaller exponent. We consider various possible explanations of this phenomenon, and settle on a modification of the Meiss-Ott Markov tree model that takes into account quantum limitations on the flux through a turnstile between regions corresponding to states on the tree. Further work is needed to better understand the quantum behavior.

Wavelet Tree Support Detection for Compressed Sensing MRI Reconstruction

A priori knowledge of the signal/image support based on its statistical and structural information in the transformed domain improves the quality of compressed sensing (CS) reconstruction. Hidden Markov tree models the wavelet domain support of magnetic resonance images obtained from undersampled k -space data very well. With the support information, parent–child pairs in the wavelet tree are detected accurately, and hence, iterative regularization problems for CS-based magnetic resonance imaging reconstruction are solved with high throughputs. Simulation results with artificial and real MRI datasets show significant improvements over existing methods in terms of just noticeable difference scanning besides other objective and subjective metrics.

A hidden Markov tree model for testing multiple hypotheses corresponding to Gene Ontology gene sets

BackgroundTesting predefined gene categories has become a common practice for scientists analyzing high throughput transcriptome data. A systematic way of testing gene categories leads to testing hundreds of null hypotheses that correspond to nodes in a directed acyclic graph. The relationships among gene categories induce logical restrictions among the corresponding null hypotheses. An existing fully Bayesian method is powerful but computationally demanding.ResultsWe develop a computationally efficient method based on a hidden Markov tree model (HMTM). Our method is several orders of magnitude faster than the existing fully Bayesian method. Through simulation and an expression quantitative trait loci study, we show that the HMTM method provides more powerful results than other existing methods that honor the logical restrictions.ConclusionsThe HMTM method provides an individual estimate of posterior probability of being differentially expressed for each gene set, which can be useful for result interpretation. The R package can be found on https://github.com/k22liang/HMTGO.

The NSCT-HMT Model of Remote Sensing Image Based on Gaussian-Cauchy Mixture Distribution

The nonsubsampled Contourlet transform (NSCT) not only retains the characteristics of Contourlet transform, but also has the good characteristic of shift-invariance, which plays a significant role in denoising, fusion, and segmentation of texture-rich images. The NSCT not only retains the properties of Contourlet transform, but also has the important property of shift-invariance, which plays a significant role in image processing, such as denoising, fusion, and segmentation of texture-rich images. This paper proposes a Gaussian-Cauchy mixture distribution-based NSCT hidden Markov tree model (GC-NSCT-HMT). The specific form of Gaussian-Cauchy mixture distribution is determined by the kurtosis of the NSCT coefficients in each subband. First, we study the probability density distribution of the remote sensing image NSCT coefficients and then propose the Gaussian-Cauchy mixture distribution, which can adaptively adjust according to the statistical property of NSCT coefficients through a balance function. Experimental results show that the proposed mixture distribution can achieve a good imitative effect to the NSCT coefficients. Second, we study the marginal statistical property and the joint statistical property of the NSCT coefficients, the persistence and aggregation properties of them are also studied in depth. We find that the ‘father’ NSCT coefficient can transfers to its son coefficients through a tree structure. Third, we combine the above conclusions with the hidden Markov tree model (HMT) and the GC-NSCT-HMT model is proposed. Finally, we apply our model to remote sensing image denoising. The subjective and objective experimental results demonstrate the feasibility of the proposed method.

Tensors, Learning, and “Kolmogorov Extension” for Finite-Alphabet Random Vectors

Estimating the joint probability mass function (PMF) of a set of random variables lies at the heart of statistical learning and signal processing. Without structural assumptions, such as modeling the variables as a Markov chain, tree, or other graphical model, joint PMF estimation is often considered mission impossible - the number of unknowns grows exponentially with the number of variables. But who gives us the structural model? Is there a generic, `non-parametric' way to control joint PMF complexity without relying on a priori structural assumptions regarding the underlying probability model? Is it possible to discover the operational structure without biasing the analysis up front? What if we only observe random subsets of the variables, can we still reliably estimate the joint PMF of all? This paper shows, perhaps surprisingly, that if the joint PMF of any three variables can be estimated, then the joint PMF of all the variables can be provably recovered under relatively mild conditions. The result is reminiscent of Kolmogorov's extension theorem - consistent specification of lower-dimensional distributions induces a unique probability measure for the entire process. The difference is that for processes of limited complexity (rank of the high-dimensional PMF) it is possible to obtain complete characterization from only three-dimensional distributions. In fact not all three-dimensional PMFs are needed; and under more stringent conditions even two-dimensional will do. Exploiting multilinear algebra, this paper proves that such higher-dimensional PMF completion can be guaranteed - several pertinent identifiability results are derived. It also provides a practical and efficient algorithm to carry out the recovery task. Judiciously designed simulations and real-data experiments on movie recommendation and data classification are presented to showcase the effectiveness of the approach.

Universal exponent for transport in mixed Hamiltonian dynamics.

We compute universal distributions for the transition probabilities of a Markov model for transport in the mixed phase space of area-preserving maps and verify that the survival probability distribution for trajectories near an infinite island-around-island hierarchy exhibits, on average, a power-law decay with exponent γ=1.57. This exponent agrees with that found from simulations of the Hénon and Chirikov-Taylor maps. This provides evidence that the Meiss-Ott Markov tree model describes the transport for mixed systems.

Remote Sensing Image Change Detection Based on NSCT-HMT Model and Its Application.

Traditional image change detection based on a non-subsampled contourlet transform always ignores the neighborhood information’s relationship to the non-subsampled contourlet coefficients, and the detection results are susceptible to noise interference. To address these disadvantages, we propose a denoising method based on the non-subsampled contourlet transform domain that uses the Hidden Markov Tree model (NSCT-HMT) for change detection of remote sensing images. First, the ENVI software is used to calibrate the original remote sensing images. After that, the mean-ratio operation is adopted to obtain the difference image that will be denoised by the NSCT-HMT model. Then, using the Fuzzy Local Information C-means (FLICM) algorithm, the difference image is divided into the change area and unchanged area. The proposed algorithm is applied to a real remote sensing data set. The application results show that the proposed algorithm can effectively suppress clutter noise, and retain more detailed information from the original images. The proposed algorithm has higher detection accuracy than the Markov Random Field-Fuzzy C-means (MRF-FCM), the non-subsampled contourlet transform-Fuzzy C-means clustering (NSCT-FCM), the pointwise approach and graph theory (PA-GT), and the Principal Component Analysis-Nonlocal Means (PCA-NLM) denosing algorithm. Finally, the five algorithms are used to detect the southern boundary of the Gurbantunggut Desert in Xinjiang Uygur Autonomous Region of China, and the results show that the proposed algorithm has the best effect on real remote sensing image change detection.

Microcalcification diagnosis in digital mammography using extreme learning machine based on hidden Markov tree model of dual-tree complex wavelet transform

Abstract Diagnosis of benign and malignant microcalcifications in digital mammography using Computer-aided Diagnosis (CAD) system is critical for the early diagnosis of breast cancer. Wavelet transform based diagnosis methods are effective to accomplish this task, but limited by representing the correlation within each wavelet scale, these methods neglect the correlation between wavelet scales. In this paper, we apply the hidden Markov tree model of dual-tree complex wavelet transform (DTCWT-HMT) for microcalcification diagnosis in digital mammography. DTCWT-HMT can effectively capture the correlation between different wavelet coefficients and model the statistical dependencies and non-Gaussian statistics of real signals, is used to characterize microcalcifications for the diagnosis of benign and malignant cases. The combined features which consist of the DTCWT-HMT features and the DTCWT features are optimized by genetic algorithm (GA). Extreme learning machine (ELM), an efficient learning theory is employed as the classifier to diagnose the benign and malignant microcalcifications. The validity of the proposed method is evaluated on the Nijmegen, MIAS and DDSM datasets using area under curve (AUC) of receiver operating characteristic (ROC). The AUC values of 0.9856, 0.9941 and 0.9168 of the proposed method are achieved on Nijmegen, MIAS and DDSM, respectively. We compare the proposed method with state-of-the-art diagnosis methods, and the experimental results show the effectiveness of the proposed method for the diagnosis of the benign and malignant microcalcifications in mammograms in terms of the accuracy and stability.

Image denoising in dual contourlet domain using hidden Markov tree models

Used in a wide variety of transform based statistical image processing techniques, the hidden Markov tree (HMT) model with Gaussian mixtures is typically employed to capture the intra-scale and inter-scale dependencies between the magnitudes of the transform coefficients. But, the conventional model does not consider the signs of the transform coefficients. In this paper, a new HMT model which exploits mixtures of one-sided exponential densities is used to consider the signs of transform coefficients. The present study has two main contributions: 1) for the first time, HMT with mixtures of one-sided exponential densities is used to denoise images, and 2) a new efficient model formed by two one-sided exponential densities and one Gaussian density is proposed. In addition, the proposed method uses the dual contourlet transform (DCT) which is formed by the combination of the directional filter bank (DFB) and the dual tree complex wavelet transform (DTCWT). This transform is (nearly) shift-invariant and is computationally less expensive than the NSCT (nonsubsampled contourlet transform). Thus, it is fast and efficient when applied to image processing tasks. Experimental results on several standard grayscale images show that the proposed method is superior to some state-of-the-art denoising techniques in terms of both subjective and objective criteria.

Model-Based Nonuniform Compressive Sampling and Recovery of Natural Images Utilizing a Wavelet-Domain Universal Hidden Markov Model

In this paper, a novel model-based compressive sampling (CS) technique for natural images is proposed. Our algorithm integrates a universal hidden Markov tree (uHMT) model, which captures the relation among the sparse wavelet coefficients of images, into both sampling and recovery steps of CS. At the sampling step, we employ the uHMT model to devise a nonuniformly sparse measurement matrix $\boldsymbol{\Phi }_{\text{uHMT}}$ . In contrast to the conventional CS sampling matrices, such as dense Gaussian, Bernoulli or uniformly sparse matrices that are oblivious to the signal model and the correlation among the signal coefficients, the proposed $\boldsymbol{\Phi }_{\text{uHMT}}$ is designed based on the signal model and samples the coarser wavelet coefficients with higher probabilities and more sparse wavelet coefficients with lower probabilities. At the recovery step, we integrate the uHMT model into two state-of-the-art Bayesian CS recovery schemes. Our simulation results confirm the superiority of our proposed HMT model-based nonuniform compressive sampling and recovery , referred to as uHMT-NCS , over other model-based CS techniques that solely consider the signal model at the recovery step. This paper is distinguished from other model-based CS schemes in that we take a novel approach to simultaneously integrating the signal model into both CS sampling and recovery steps. We show that such integration greatly increases the performance of the CS recovery, which is equivalent to reducing the required number of samples for a given reconstruction quality.

Forecasting time-to-failure of machine using hybrid Neuro-genetic algorithm – a case study in mining machinery

Forecasting of time-to-failure is an important aspect of a mining machine for the performance assessment, fault detection and schedule maintenance. The knowledge of failure time allows more defined arrangement of preventive maintenance. Traditional methods, including lifetime distribution models, fault tree analysis and Markov models, have a limitation of assuming a specific statistical distribution function to fit the failure time data. In this study, a hybrid data-driven method using neural network and genetic algorithm is proposed to forecast failure time. The forecasting model was developed using neural network algorithm and all the neural network parameters, i.e. input nodes, hidden nodes and the learning algorithms, are selected automatically using the genetic algorithm. The developed model was validated using the failure data of a mining machine. A case study was conducted investigating a load-haul-dump machine (LHD) in the mining industry. Failure historical data for the LHD machine were collected, and cumulative failure time was calculated for time-to-failure forecasting. Study results demonstrate that the developed model performs satisfactory in the prediction of next failure time. A comparative study reveals that the proposed method performs better than existing methods.

Texture Segmentation Using Laplace Distribution-Based Wavelet-Domain Hidden Markov Tree Models

Multiresolution models such as the wavelet-domain hidden Markov tree (HMT) model provide a powerful approach for image modeling and processing because it captures the key features of the wavelet coefficients of real-world data. It is observed that the Laplace distribution is peakier in the center and has heavier tails compared with the Gaussian distribution. Thus we propose a new HMT model based on the two-state, zero-mean Laplace mixture model (LMM), the LMM-HMT, which provides significantly potential for characterizing real-world textures. By using the HMT segmentation framework, we develop LMM-HMT based segmentation methods for image textures and dynamic textures. The experimental results demonstrate the effectiveness of the introduced model and segmentation methods.

Robust video fingerprinting scheme based on contourlet hidden Markov tree model

Video fingerprints are feature vectors that uniquely characterize a video clip and can be used for video indexing and copyright applications. This paper presents a novel video fingerprinting method based on the Contourlet hidden Markov tree model and Singular Value Decomposition. The Contourlet transform is a two-dimensional extension of the wavelet transform using multiscale and directional filter banks. It effectively captures the smooth contours that are the dominant features in natural images. The Contourlet HMT model can capture all inter-scale, inter-direction, and inter-location dependencies of the contourlet coefficients using a few statistics parameters. These parameters are robust against common content- preserving operations such as lossy compression, additive noise, filtering etc. We introduce SVD to compress the parameter matrix for generating the video fingerprint. The performance of the proposed fingerprint is experimentally evaluated and compared to the Centroid of Gradient Orientations based method. The proposed method is shown to have a better overall performance in robustness and video identification.

Denoising in Wavelet Domain Using Probabilistic Graphical Models

Denoising of real world images that are degraded by Gaussian noise is a long established problem in statistical signal processing. The existing models in time-frequency domain typically model the wavelet coefficients as either independent or jointly Gaussian. However, in the compression arena, techniques like denoising and detection, states the need for models to be non-Gaussian in nature. Probabilistic Graphical Models designed in time-frequency domain, serves the purpose for achieving denoising and compression with an improved performance. In this work, Hidden Markov Model (HMM) designed with 2D Discrete Wavelet Transform (DWT) is proposed. A comparative analysis of proposed method with different existing techniques: Wavelet based and curvelet based methods in Bayesian Network domain and Empirical Bayesian Approach using Hidden Markov Tree model for denoising has been presented. Results are compared in terms of PSNR and visual quality.

Polar Coding for Secret-Key Generation

Practical implementations of secret-key generation are often based on sequential strategies, which handle reliability and secrecy in two successive steps, called reconciliation and privacy amplification. In this paper, we propose an alternative approach based on polar codes that jointly deals with reliability and secrecy. Specifically, we propose secret-key capacity-achieving polar coding schemes for the following models: (i) the degraded binary memoryless source (DBMS) model with rate-unlimited public communication, (ii) the DBMS model with one-way rate-limited public communication, (iii) the 1-to-m broadcast model and (iv) the Markov tree model with uniform marginals. For models (i) and (ii) our coding schemes remain valid for non-degraded sources, although they may not achieve the secret-key capacity. For models (i), (ii) and (iii), our schemes rely on pre-shared secret seed of negligible rate; however, we provide special cases of these models for which no seed is required. Finally, we show an application of our results to secrecy and privacy for biometric systems. We thus provide the first examples of low-complexity secret-key capacity-achieving schemes that are able to handle vector quantization for model (ii), or multiterminal communication for models (iii) and (iv).

Extended Shearlet HMT Model-Based Image Denoising Using BKF Distribution

Images are often corrupted by noise in the procedures of image acquisition and transmission. It is a challenging work to design an edge-preserving image denoising scheme. Extended discrete Shearlet transform (extended DST) is an effective multi-scale and multi-direction analysis method; it not only can exactly compute the Shearlet coefficients based on a multiresolution analysis, but also can represent images with very few coefficients. In this paper, we propose a new image denoising approach in extended DST domain, which combines hidden Markov tree (HMT) model and Bessel K Form (BKF) distribution. Firstly, the marginal statistics of extended DST coefficients are studied, and their distribution is analytically calculated by modeling extended DST coefficients with BKF probability density function. Then, an extended Shearlet HMT model is established for capturing the intra-scale, inter-scale, and cross-orientation coefficients dependencies. Finally, an image denoising approach based on the extended Shearlet HMT model is presented. Extensive experimental results demonstrate that our extended Shearlet HMT denoising approach can obtain better performances in terms of both subjective and objective evaluations than other state-of-the-art HMT denoising techniques. Especially, the proposed approach can preserve edges very well while removing noise.

The Application of Wavelet-Domain Hidden Markov Tree Model in Diabetic Retinal Image Denoising.

The wavelet-domain Hidden Markov Tree Model can properly describe the dependence and correlation of fundus angiographic images’ wavelet coefficients among scales. Based on the construction of the fundus angiographic images Hidden Markov Tree Models and Gaussian Mixture Models, this paper applied expectation-maximum algorithm to estimate the wavelet coefficients of original fundus angiographic images and the Bayesian estimation to achieve the goal of fundus angiographic images denoising. As is shown in the experimental result, compared with the other algorithms as mean filter and median filter, this method effectively improved the peak signal to noise ratio of fundus angiographic images after denoising and preserved the details of vascular edge in fundus angiographic images.

Large-Scale Empirical Tests of the Markov Tree Model

The Markov Tree model is a discrete-time option pricing model that accounts for short-term memory of the underlying asset. In this work, we compare the empirical performance of the Markov Tree model against that of the Black-Scholes model and Heston’s stochastic volatility model. Leveraging a total of five years of individual equity and index option data, and using three new methods for fitting the Markov Tree model, we find that the Markov Tree model makes smaller out-of-sample hedging errors than competing models. This comparison includes versions of Markov Tree and Black-Scholes models in which volatilities are strike- and maturity-dependent. Visualizing the errors over time, we find that the Markov Tree model yields more accurate and less risky single instrument hedges than Heston’s stochastic volatility model. A statistical resampling method indicates that the Markov Tree model’s superior hedging performance is due to its robustness with respect to noise in option data.

Real-time classification of humans versus animals using profiling sensors and hidden Markov tree model

Linear pyroelectric array sensors have enabled useful classifications of objects such as humans and animals to be performed with relatively low-cost hardware in border and perimeter security applications. Ongoing research has sought to improve the performance of these sensors through signal processing algorithms. In the research presented here, we introduce the use of hidden Markov tree (HMT) models for object recognition in images generated by linear pyroelectric sensors. HMTs are trained to statistically model the wavelet features of individual objects through an expectation–maximization learning process. Human versus animal classification for a test object is made by evaluating its wavelet features against the trained HMTs using the maximum-likelihood criterion. The classification performance of this approach is compared to two other techniques; a texture, shape, and spectral component features (TSSF) based classifier and a speeded-up robust feature (SURF) classifier. The evaluation indicates that among the three techniques, the wavelet-based HMT model works well, is robust, and has improved classification performance compared to a SURF-based algorithm in equivalent computation time. When compared to the TSSF-based classifier, the HMT model has a slightly degraded performance but almost an order of magnitude improvement in computation time enabling real-time implementation.