Markov Tree Research Articles

Thirty years of turnstiles and transport.

To characterize transport in a deterministic dynamical system is to compute exit time distributions from regions or transition time distributions between regions in phase space. This paper surveys the considerable progress on this problem over the past thirty years. Primary measures of transport for volume-preserving maps include the exiting and incoming fluxes to a region. For area-preserving maps, transport is impeded by curves formed from invariant manifolds that form partial barriers, e.g., stable and unstable manifolds bounding a resonance zone or cantori, the remnants of destroyed invariant tori. When the map is exact volume preserving, a Lagrangian differential form can be used to reduce the computation of fluxes to finding a difference between the actions of certain key orbits, such as homoclinic orbits to a saddle or to a cantorus. Given a partition of phase space into regions bounded by partial barriers, a Markov tree model of transport explains key observations, such as the algebraic decay of exit and recurrence distributions.

Dynamic texture based smoke detection using Surfacelet transform and HMT model

To detect smoke regions from video clips, a novel dynamic texture descriptor is proposed with Surfacelet transform and hidden Markov tree (HTM) model. The image sequence is multi-scale decomposed by a pyramid model, and the signals are decomposed to different directions using 3D directional filter banks. Then a 3D HMT model is built for obtained coefficients from Surfacelet transform with both Gaussian mixture model and scale continuity model. Parameters of the HMT model are estimated through expectation maximization algorithm, and the joint probability density is determined as the dynamic texture feature value. Support vector machine (SVM) classifier is trained with samples including smoke and non-smoke videos. For input image sequence, the joint probability density of each divided unit 3D block is taken as the input of SVM to decide whether there is smoke. The new dynamic texture descriptor takes image sequence as a multidimensional volumetric data, i.e., considering both spatial and temporal information of coefficients into one model. In experiments, existing texture descriptors of gray level co-occurrence matrix (GLCM), local binary pattern (LBP) and Wavelet are implemented and used for comparison. Results from many real smoke videos have proved that the new dynamic texture descriptor can obtain higher detection accuracy.

Color image segmentation using PDTDFB domain hidden Markov tree model

The pyramidal dual-tree directional filter bank (PDTDFB) transform is a new image decomposition, which has many advantages, such as multiscale and multidirectional transform, efficient implementation, high angular resolution, low redundant ratio, and shiftable subbands. In this paper, we present a new color image segmentation algorithm based on PDTDFB domain hidden Markov tree (HMT) model. Firstly, the joint statistics and mutual information of the PDTDFB coefficients are studied. Then, the PDTDFB coefficients are modeled using a HMT model with Gaussian mixtures, which can effectively capture the intra-scale, inter-scale, and inter-direction dependencies. Finally, a color image segmentation using PDTDFB domain HMT model is developed, in which expectation–maximization (EM) parameter estimation, Bayesian multiscale raw segmentation, context based multiscale fusion, and majority-vote based color component fusion are used. Experimental evidence shows that the proposed color image segmentation algorithm has very effective segmentation results in comparison with the state-of-the-art segmentation methods recently proposed in the literature.

Iron Supplementation Adjunct to Erythropoiesis Stimulating Agents Is Cost Saving for Chemotherapy-Related Anemia in the Era of Biosimilars

▪Background: International guidelines recommend erythropoiesis stimulating agents (ESA) to improve chemotherapy-related anemia (CRA), however, two meta-analyses proved that intravenous iron (II) improves the chance of obtaining a response to ESA by 28% (Gafter-Gvili 2013, Petrelli 2012). Recently, biosimilar ESAs have been approved for CRA, we therefore aimed at comparing the cost-effectiveness of different therapeutic strategies for CRA eventually including II and/or biosimilar ESAs.Methods: A decision model was built comparing 5 strategies: no ESA, brand ESA, brand ESA plus II, biosimilar ESA, biosimilar ESA plus II. Ferric gluconate was assumed to be administered 125 mg per week for 6 weeks overall: 4 infusions were planned in days different from chemotherapy administration. ESA was started at hemoglobin values lower than 11 g/dl. The model included a Markov tree of 13 health states representing hemoglobin level during 26 therapy weeks. Weekly probability of hemoglobin improvement by 1 g/dL was estimated to be 10% with ESA and 15% with ESA plus II but null without ESA. The efficacy of biosimilar ESA was assumed to be the same as ESA. Weekly probability of death was assumed to be 0.4% (Pedrazzoli 2008). The rate of severe events during II infusion was assumed to be 0.2% per week without fatal events. Quality of life at different hemoglobin levels was driven from literature. The economic analysis was run in the perspective of the Health Care System and of the society. II administration was charged €50 and blood transfusion €400. Indirect costs for iron infusions and transfusions planned in days not devoted to chemotherapy was estimated to be €100 for transportation and care-giver time. Based on local data, the per-unit cost of biosimilar ESA versus brand ESA was considered to be 1 in 5.All the analyses were run TreeAgePro2014. Microsimulations and first-order MonteCarlo analysis were run.Results: ESA improve quality-adjusted survival of patients from 14.51 to 14.82 quality-adjusted weeks but II adjunct increased the gain to 15.20 weeks. In the perspective of the health-care system, the management of cancer-related anemia without ESA costs €1,550, while ESA therapy increased the costs by €618 (biosimilars) and €2,933 (brand); ESA plus II increased the costs by €359 and €2,437, respectively. Therefore, the adjunct of II reduced overall health-care costs by €259 in the biosimilar strategy and €496 in the brand ESA strategy. Societal costs similarly increased with ESA use, but the increment was lower: €584 with biosimilar ESA and €2,866 with brand ESA. II allowed to achieve minimal savings in the biosimilar strategy, while savings were €288 in the brand ESA strategy. Savings to the health-care system and to the society were even higher (further €300 to the healthcare-system and €90 to the society) in the hypothesis that liposomial oral iron (30 mg per day for 60 days) achieved similar results as II, at €1 per day charged to the patient (in Italy liposomal iron it is not refunded). Ferric carboxymaltose 750 mg single administration at a cost of €280 might compete with multiple ferric gluconate administrations. Finally, we explored the efffect of threshold hemoglobin: starting ESA at hemoglobin levels lower than 10 g/dl instead of 11 g/dl allowed to reduce health-care costs of ESA therapy by €172, but quality of life was increased by only 0.14 and 0.59 weeks, without and with II, respectively.Conclusions: Rational allocation of health-care resources imposes to choose the most convenient therapeutic strategy among those recommended by practice guidelines. Intravenous iron allows to save health-care and society resources and to improve quality of life by a more rapid hematopoietic response to ESA. Different iron formulations need to be tested in association with ESA in this setting in order to improve the efficiency of avilable therapeutic strategies. Cost-effectiveness analyses should be shared by clinicians and hospital pharmacy to adopt the most effective and efficient therapeutic strategies. DisclosuresNo relevant conflicts of interest to declare.

Uniform Chernoff and Dvoretzky-Kiefer-Wolfowitz-Type Inequalities for Markov Chains and Related Processes

We observe that the technique of Markov contraction can be used to establish measure concentration for a broad class of noncontracting chains. In particular, geometric ergodicity provides a simple and versatile framework. This leads to a short, elementary proof of a general concentration inequality for Markov and hidden Markov chains, which supersedes some of the known results and easily extends to other processes such as Markov trees. As applications, we provide a Dvoretzky-Kiefer-Wolfowitz-type inequality and a uniform Chernoff bound. All of our bounds are dimension-free and hold for countably infinite state spaces.

Uniform Chernoff and Dvoretzky-Kiefer-Wolfowitz-Type Inequalities for Markov Chains and Related Processes

We observe that the technique of Markov contraction can be used to establish measure concentration for a broad class of noncontracting chains. In particular, geometric ergodicity provides a simple and versatile framework. This leads to a short, elementary proof of a general concentration inequality for Markov and hidden Markov chains, which supersedes some of the known results and easily extends to other processes such as Markov trees. As applications, we provide a Dvoretzky-Kiefer-Wolfowitz-type inequality and a uniform Chernoff bound. All of our bounds are dimension-free and hold for countably infinite state spaces.

An edge detection scheme based on least squares support vector machine in a contourlet HMT domain

In this paper, we have presented a new and effective edge detection scheme based on least squares support vector machine (LS-SVM) classification in a contourlet Hidden Markov Tree Model (contourlet HMT). First, the input noisy image is decomposed into coarser and finer coefficients using a contourlet HMT transform to derive an efficient multiscale and multidirectional image representation. Second, the feature vector is performed through spatial regularity in a contourlet HMT domain, and the coarser coefficients classified using LS-SVM classifier into two classes: noise coefficients and edge coefficients. Next, all noisy contourlet HMT coefficients are well denoised by the BayesShrink method.Finally, the denoised coefficients and edge coefficients are fused using the weighted average rule, and the inverse contourlet HMT is applied to obtain the edge image.Experimental results demonstrate that our scheme can attain improved performance over state-of-the-art edge detection approaches, both qualitatively and quantitatively. Tests were performed on several images from the Berkeley dataset corrupted with Gaussian noise and on other images such as a cameraman, pepper and medical images. The results illustrate that the performance of the proposed scheme is stable.

Automated defect detection in textured materials using wavelet-domain hidden Markov models

An approach that addresses defect detection in textured surfaces based on the wavelet-domain hidden Markov tree (HMT) model is proposed. The proposed scheme includes two successive stages, i.e., training and inspection. During the training process, an HMT for the wavelet transform (WT) of an a priori acquired defect-free template image is modeled using the expectation-maximization (EM) algorithm. With the trained HMT, a log-likelihood map (LLM) that consists of the likelihood of each coefficient can be efficiently constructed. This LLM provides a good classifier for discriminating defects from regular textures. By comparing the LLM of any defective sample under inspection with that of the template, a thresholding process can typically set the coefficients corresponding to the regular texture background to zero, while preserving those corresponding to defective regions. Therefore, in a reconstructed image obtained by the inverse two-dimensional WT of the modified coefficients, the texture patterns will be significantly eliminated, whereas the defective regions will be distinctly highlighted. The performance of the proposed method has been extensively evaluated by a variety of samples with different defect types, shapes, sizes, and texture backgrounds. Experimental results in comparison with other methods demonstrate the effectiveness of the proposed method on defect detection in textured surfaces.

Localizing the latent structure canonical uncertainty: entropy profiles for hidden Markov models

This report addresses state inference for hidden Markov models. These models rely on unobserved states, which often have a meaningful interpretation. This makes it necessary to develop diagnostic tools for quantification of state uncertainty. The entropy of the state sequence that explains an observed sequence for a given hidden Markov chain model can be considered as the canonical measure of state sequence uncertainty. This canonical measure of state sequence uncertainty is not reflected by the classic multivariate state profiles computed by the smoothing algorithm, which summarizes the possible state sequences. Here, we introduce a new type of profiles which have the following properties: (i) these profiles of conditional entropies are a decomposition of the canonical measure of state sequence uncertainty along the sequence and makes it possible to localize this uncertainty, (ii) these profiles are univariate and thus remain easily interpretable on tree structures. We show how to extend the smoothing algorithms for hidden Markov chain and tree models to compute these entropy profiles efficiently.

The Method of Quaternions Wavelet Image Denoising

Based on traditional wavelet image denoising model, studies the quaternion, the application of wavelet transform in image denoising, quaternions are given three on the wavelet transform domain image denoising model and algorithm: (1) based on quaternion wavelet hidden markov tree model of image denoising; (2) based on quaternion wavelet transform non-gaussian bivariate distribution image denoising algorithm of bayesian statistical model; (3) based on quaternion mixing statistical model of wavelet image denoising. Experiments show that: in this paper, the denoising effect of these methods, in both the peak signal-to-noise ratio and the visual effects are better than many classic denoising algorithms.

Reconstruction of Wavelet Coefficients

A comparative study of different methods of reconstruction of wavelet coefficients is presented. The following are the different techniques for the reconstruction of wavelet coefficients. To start with, we show how to design and construct Daubechies four coefficient wavelet system which are orthogonal and compactly supported wavelets. Then we outline the multi resolution analysis of wavelets using Mallat transform. Multi resolution analysis can be illustrated by the decomposition and reconstruction of wavelet system using Laplacian Pyramid. To construct wavelet systems with finite support and regularity using orthonormal and interpolariting units, only multicomponent wavelets are possible. When image function is expressed in terms of scaling functions and wavelet functions of higher resolution, we need to consider only few wavelet coefficients and wavelet coefficients are dominant only near edges. The wavelet coefficient near edges can be estimated using wavelet transform maxima and statistical inference of coefficients using Markov tree model. An alternate method is the reconstruction of wavelet coefficients using total variation minimisation. If we use thresholding, so that when we neglect wavelet coefficients having values less than a threshold value there is ringing across edges. Hence we propose an improved algorithm of reconstruction of wavelet coefficients using zero padding and cycle spinning. PSNR of images with wavelet based interpolation and denoising by cycle spinning is moderately high.

AIRWAY LABELING USING A HIDDEN MARKOV TREE MODEL.

We present a novel airway labeling algorithm based on a Hidden Markov Tree Model (HMTM). We obtain a collection of discrete points along the segmented airway tree using particles sampling [1] and establish topology using Kruskal's minimum spanning tree algorithm. Following this, our HMTM algorithm probabilistically assigns labels to each point. While alternative methods label airway branches out to the segmental level, we describe a general method and demonstrate its performance out to the subsubsegmental level (two generations further than previously published approaches). We present results on a collection of 25 computed tomography (CT) datasets taken from a Chronic Obstructive Pulmonary Disease (COPD) study.

Image denoising in extended Shearlet domain using hidden Markov tree models

Denoising of images is one of the most basic tasks of image processing. 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 provide nearly optimal approximation for a piecewise smooth function. In this paper, a new image denoising approach in extended Shearlet domain using hidden Markov tree (HMT) model is proposed. Firstly, the joint statistics and mutual information of the extended DST coefficients are studied. Then, the extended DST coefficients are modeled using an HMT model with Gaussian mixtures, which can effectively capture the intra-scale and inter-scale dependencies. Finally, the extended Shearlet HMT model is applied to image denoising. Extensive experimental results demonstrate that our extended Shearlet HMT denoising method can obtain better performances in terms of both subjective and objective evaluations than other state-of-the-art HMT denoising techniques. Especially, the proposed method can preserve edges very well while removing noise.

Multi-scale discriminant saliency with wavelet-based Hidden Markov Tree modelling

Supposed saliency is a binary classification between centre and surround classes, saliency value is measured as their discriminant power. As the features are defined by sizes of chosen windows, a saliency value at each location is varied accordingly. This paper proposes computing saliency as discriminant power in multiple dyadic scales of Wavelet Hidden Markov Tree (HMT), in which two consecutive dyadic scales provide surrounding and central features, organized in a quad-tree structure. Their discriminant power is estimated as maximum a posterior probability (MAP) by Expectation-Maximization (EM) iterations. Then, a final saliency value is the maximum discriminant power generated among these scales. Standard quantitative tools and qualitative assessments are used for evaluating the proposed multi-scale discriminant saliency (MDIS) against the well-know information based approach AIM on its image collection with eye-tracking data. Simulation results are presented and analysed to verify the validity of MDIS as well as point out its limitation for further research direction.

Pricing Options Based on Trinomial Markov Tree

A trinomial Markov tree model is studied for pricing options in which the dynamics of the stock price are modeled by the first-order Markov process. Firstly, we construct a trinomial Markov tree with recombining nodes. Secondly, we give an algorithm for estimating the risk-neutral probability and provide the condition for the existence of a validation risk-neutral probability. Thirdly, we propose a method for estimating the volatilities. Lastly, we analyze the convergence and sensitivity of the pricing method implementing trinomial Markov tree. The result shows that, compared to binomial Markov tree, the proposed model is a natural combining tree and, while changing the probability of the node, it is still combining, so the computation is very fast and very easy to be implemented.

A novel optimization design approach for Contourlet directional filter banks

A Contourlet transform, an expansion of a wavelet transform, is a double filter bank structure composed of Laplacian Pyramid and directional filter banks. Several wavelet filters of preferable performance have been developed for wavelet transforms, e.g. CDF (Cohen, Daubechies and Feauveau) 9/7 filter. However, there is still only a limited number of wavelet filters applicable for Contourlet transforms. Therefore, it has become an urgent issue to find effective contourlet filters and design methods in the field of multiscale geometric analysis. In order to design a new directional filter bank for Contourlet transforms, this paper uses parametric modeling to obtain a novel PKVA (See-May Phoong, Chai W. Kim, P. P. Vaidyanathan, and Rashid Ansari) filter, by first implementing Chebyshev best uniform approximation, and then reaching the optimal solution by means of Parks-McClellan algorithm. Using Brodatz standard texture image database for test images, and using image denoising treated with hidden Markov tree (HMT) models in the Contourlet domain, the optimal PKVA filter was obtained on the basis of the peak signal to noise ratio (PSNR) maximum criterion with human visual properties considered. Experiment results show that the image denoising performance of our filter is better than that of Po and Do’s. The PSNR obtained from the experiment is 1.011449 higher than that of Po and Do’s in average. Therefore, Contourlet transforms using the proposed PKVA filter as DFB can ensure that the local error in images is of a uniform minimum value, and that good overall visual effect can be achieved.

A Max-Product EM Algorithm for Reconstructing Markov-Tree Sparse Signals From Compressive Samples

We propose a Bayesian expectation-maximization (EM) algorithm for reconstructing Markov-tree sparse signals via belief propagation. The measurements follow an underdetermined linear model where the regression-coefficient vector is the sum of an unknown approximately sparse signal and a zero-mean white Gaussian noise with an unknown variance. The signal is composed of large- and small-magnitude components identified by binary state variables whose probabilistic dependence structure is described by a Markov tree. Gaussian priors are assigned to the signal coefficients given their state variables and the Jeffreys' noninformative prior is assigned to the noise variance. Our signal reconstruction scheme is based on an EM iteration that aims at maximizing the posterior distribution of the signal and its state variables given the noise variance. We construct the missing data for the EM iteration so that the complete-data posterior distribution corresponds to a hidden Markov tree (HMT) probabilistic graphical model that contains no loops and implement its maximization (M) step via a max-product algorithm. This EM algorithm estimates the vector of state variables as well as solves iteratively a linear system of equations to obtain the corresponding signal estimate. We select the noise variance so that the corresponding estimated signal and state variables obtained upon convergence of the EM iteration have the largest marginal posterior distribution. We compare the proposed and existing state-of-the-art reconstruction methods via signal and image reconstruction experiments.

非下采样Contourlet HMT模型

The non-subsampled Contourlet transform (NSCT) has not only characteristics of multi-scale, multidirection and anisotropy, like traditional wavelet transform and Contourlet transform, but also the good characteristics of shift-invariant. We draw the conclusion that the directional subband coefficients also have persistence and aggregation through studying the coefficients of the NSCT. On the basis of HMT, we establish a novel non-subsampled Contourlet transform domain hidden Markov tree model, NSCT-HMT, and give the parameters structure of the model as well as the training method of the model parameters. Finally, we apply the proposed model to image denoising, and achieve a good simulation effect.

Tree‐structured complex wavelet‐based Bayesian compressive sensing method

Using complex wavelets, the tree-structured complex wavelet Bayesian compressive sensing method is proposed. The hidden Markov tree is used for inter-scale relations of wavelet coefficients. The spike-slab distribution is considered for the prior. From simulation results, the number of measurements and the value of reconstruction error reduce by 25% and 65%, respectively.

Sample Distortion for Compressed Imaging

We propose the notion of a sample distortion (SD) function for independent and identically distributed (i.i.d) compressive distributions to fundamentally quantify the achievable reconstruction performance of compressed sensing for certain encoder-decoder pairs at a given sampling ratio. Two lower bounds on the achievable performance and the intrinsic convexity property is derived. A zeroing procedure is then introduced to improve non convex SD functions. The SD framework is then applied to analyse compressed imaging with a multi-resolution statistical image model using both the generalized Gaussian distribution and the two-state Gaussian mixture distribution. We subsequently focus on the Gaussian encoder-Bayesian optimal approximate message passing (AMP) decoder pair, whose theoretical SD function is provided by the rigorous analysis of the AMP algorithm. Given the image statistics, analytic bandwise sample allocation for bandwise independent model is derived as a reverse water-filling scheme. Som and Schniter's turbo message passing approach is further deployed to integrate the bandwise sampling with the exploitation of the hidden Markov tree structure of wavelet coefficients. Natural image simulations confirm that with oracle image statistics, the SD function associated with the optimized sample allocation can accurately predict the possible compressed sensing gains. Finally, a general sample allocation profile based on average image statistics not only illustrates preferable performance but also makes the scheme practical.