Wavelet-domain Hidden Markov Models Research Articles

Surface defects detection in metal materials repaired by laser surfacing of seal welds

Laser surfacing repair technology for sealing welds is widely used in metal repair. Due to welding technology and usage scenarios, process defects on the metal surface are inevitable. Therefore, ultrasonic surface wave technology is used to analyze the surface defects of metal materials. Principal Component Analysis (PCA) is used to extract the main defect signals on the metal surface, and synthetic aperture focusing technology is used to reduce imaging errors. Considering the lack of PCA in imaging defects, wavelet domain hidden Markov models (WHMM) are combined to optimize the signal, thereby improving the inspection effect of metal defects. In the test results of the relationship between the propagation distance of 316 L steel and the defect echo signal, the echo signal gradually fitted as the propagation distance increased. When the propagation distance was greater than 10 mm, the image acquisition defect signal had significant noise points. Various techniques were used to process the original echo signals of metal surface defects. The improved PCA-WHMM algorithm had significant advantages with the SNR value of the defect image increased by 13.65 % compared to PCA-WHMM. At the same time, the surface repair effects of laser surfacing 316 L metal before and after optimization were compared. The hardness, toughness, and corrosion resistance of the optimized metal were significantly improved. The proposed technological innovation combines traditional laser surfacing repair with deep learning fault diagnosis, which not only greatly improves the efficiency of fault diagnosis, but also proves that this research can effectively avoid common focus issues of laser surfacing repair technology, providing important technical reference for the application of ultrasonic technology in metal defect detection.

Wavelets and stochastic theory: Past and future

In the paper, authors report on the interdisciplinary and extremely complex link between wavelets and stochastic processes. An insight into the history of wavelets has been provided presenting the fundamental conception of wavelets, as well as wavelet theory that emerged from stochastic processes. The multiresolution analysis corresponds to the Kolmogorov system which is a regular stationary stochastic process. It presents a significant link to the measurement problem in terms of positional notation which the wavelet domain hidden Markov model should be derived from. The optimal representation arises to be an issue requiring further elaboration extended to the general measurement and wavelet frames.

Stochastic Analysis of the Time Continuum

This paper considers the time continuum of Brouwer in terms of the complex system physics. It is based upon a processual definition of real numbers which concern the measurement problem. The multiresolution hierarchy of the measurement process is represented by the time operator acting on continuous signals. The wavelet domain hidden Markov model, which recapitulates statistical properties of the hierarchy, is verified experimentally on a wide range of signal ensembles. It indicates a novel method that has already been proved to be tremendously useful in applied mathematics.

Diagnosis of design and defects in radiography of ceramic antique objects using the wavelet-domain hidden Markov models

Abstract Radiography is often the method of choice for detection of hidden design details and defects in antique ceramic objects. To maximize information extraction from the images, as well as to optimize the operators’ image interpretation, the design and defect regions should be revealed. Development of effective image enhancement methods is an important research area in industrial radiographic testing. In this study, the wavelet-domain hidden Markov models were used to improve the hidden design detail and defect(s) visualization from the radiographs of the ceramic antique objects of Samiran region. The method relies on generating the frequency components of the image and removing noise from the low contrast component by means of the Markov method. The proposed algorithm was successfully applied to the radiographic images of the antique and cultural heritage objects. The design detail visualization and defect region detection were improved whilst preserving the object edge and fine detail imaging information. Experts’ reviews showed that the design details from the dual domain reconstructed images were better visualized than the original images. Also, different defects were better detected by the application of the method to the images.

A Robust Multibit Multiplicative Watermark Decoder Using a Vector-Based Hidden Markov Model in Wavelet Domain

The vector-based hidden Markov model (HMM) is a powerful statistical model for characterizing the distribution of the wavelet coefficients, since it is capable of capturing the subband marginal distribution as well as the inter-scale and cross-orientation dependencies of the wavelet coefficients. In this paper we propose a scheme for designing a blind multibit watermark decoder incorporating the vector-based HMM in wavelet domain. The decoder is designed based on the maximum likelihood criterion. A closed-form expression is derived for the bit error rate and validated experimentally with Monte Carlo simulations. The performance of the proposed watermark detector is evaluated using a set of standard test images and shown to outperform the decoders designed based on the Cauchy or generalized Gaussian distributions without or with attacks. It is also shown that the proposed decoder is more robust against various kinds of attacks compared with the state-of-the-art methods.

Images Denoising and Enhancement Based on Dyadic Wavelet Domain Hidden Markov Models and Interpolation

Images Denoising and Enhancement Based on Dyadic Wavelet Domain Hidden Markov Models and Interpolation

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.

Quantifying self-organization with optimal wavelets

An optimal wavelet basis is used to develop a quantitative, experimentally applicable criterion for self-organization. The choice of the optimal wavelet is based on the model of self-organization in the wavelet tree. The framework of the model is founded on the wavelet-domain hidden Markov model and the optimal wavelet basis criterion for self-organization. The principle assumes increase in statistical complexity considered as the information content necessary for maximally accurate prediction of the system's dynamics. The causal states and the wavelet machine (w-machine) are defined in analogy with the ϵ-machine constructed as the unique, minimal, predictive model of the process. The method, presented here for the one-dimensional data, concurrently performs superior denoising and may be easily generalized to higher dimensions.

Artificial immune multi-objective SAR image segmentation with fused complementary features

Artificial immune systems (AIS) are the computational systems inspired by the principles and processes of the vertebrate immune system. AIS-based algorithms typically mimic the human immune system’s characteristics of learning and adaptability to solve some complicated problems. Here, an artificial immune multi-objective optimization framework is formulated and applied to synthetic aperture radar (SAR) image segmentation. The important innovations of the framework are listed as follows: (1) an efficient and robust immune, multi-objective optimization algorithm is proposed, which has the features of adaptive rank clones and diversity maintenance by K-nearest-neighbor list; (2) besides, two conflicting, fuzzy clustering validity indices are incorporated into this framework and optimized simultaneously and (3) moreover, an effective, fused feature set for texture representation and discrimination is constructed and researched, which utilizes both the Gabor filter’s ability to precisely extract texture features in low- and mid-frequency components and the gray level co-occurrence probability’s (GLCP) ability to measure information in high-frequency. Two experiments with synthetic texture images and SAR images are implemented to evaluate the performance of the proposed framework in comparison with other five clustering algorithms: fuzzy C-means (FCM), single-objective genetic algorithm (SOGA), self-organizing map (SOM), wavelet-domain hidden Markov models (HMTseg), and spectral clustering ensemble (SCE). Experimental results show the proposed framework has obtained the better performance in segmenting SAR images than other five algorithms and behaves insensitive to the speckle noise.

Asymmetry of information flow between volatilities across time scales

Conventional time series analysis, focusing exclusively on a time series at a given scale, lacks the ability to explain the nature of the data-generating process. A process equation that successfully explains daily price changes, for example, is unable to characterize the nature of hourly price changes. On the other hand, statistical properties of monthly price changes are often not fully covered by a model based on daily price changes. In this paper, we simultaneously model regimes of volatilities at multiple time scales through wavelet-domain hidden Markov models. We establish an important stylized property of volatility across different time scales. We call this property asymmetric vertical dependence. It is asymmetric in the sense that a low volatility state (regime) at a long time horizon is most likely followed by low volatility states at shorter time horizons. On the other hand, a high volatility state at long time horizons does not necessarily imply a high volatility state at shorter time horizons. Our analysis provides evidence that volatility is a mixture of high and low volatility regimes, resulting in a distribution that is non-Gaussian. This result has important implications regarding the scaling behavior of volatility, and, consequently, the calculation of risk at different time scales.

Image Denoising through Self-Organizing Feature Map Based on Wavelet-Domain HMMs

Although the Wavelet-domain hidden Markov Models (HMMs) can powerfully preserve the image edge information, it lacks local dependency information. According to the deficiency, a novel image denoising method based HMMs through the self-organizing feature map(SOFM) which exploits spatial local correlation among image neighbouring wavelet coefficients is proposed in this paper. SOFM algorithms is popular for unsupervised learning and data clustering and can capture persistence properties of wavelet coefficients. Experimental results show that the performance of the proposed method is more practicable and more effective to suppress additive white Gaussian noise and preserve the details of the image.

FRAME-BASED IMAGE DENOISING USING HIDDEN MARKOV MODEL

Wavelet-domain hidden Markov models (HMMs), and in particular, hidden Markov tree (HMT), have been recently proposed and applied to image denoising. In this paper, we present the hidden Markov model and corresponding algorithm based on frame-domain. This model can effectively capture the correlation of wavelet frame coefficients, and we apply this model for image denoising. Furthermore, two new algorithms are developed for denoising. We demonstrate the performance of our new method on some text images with very encouraging results.

SIGNAL DENOISING USING WAVELETS AND BLOCK HIDDEN MARKOV MODEL

This paper presents a new framework for signal denoising based on wavelet-domain hidden Markov models (HMMs). The new framework enables us to concisely model the statistical dependencies and non-Gaussian statistics encountered in real-world signals, and enables us to get a more reliable and local model using blocks. Wavelet-domain HMMs are designed with the intrinsic properties of wavelet transform and provide powerful yet tractable probabilistic signal models. In this paper, we propose a novel wavelet domain HMM using blocks to strike a delicate balance between improving spatial adaptability of contextual HMM (CHMM) and modeling a more reliable HMM. Each wavelet coefficient is modeled as a Gaussian mixture model, and the dependencies among wavelet coefficients in each subband are described by a context structure, then the structure is modified by blocks which are connected areas in a scale conditioned on the same context. Before denoising a signal, efficient Expectation Maximization (EM) algorithms are developed for fitting the HMMs to observational signal data. Parameters of trained HMM are used to modify wavelet coefficients according to the rule of minimizing the mean squared error (MSE) of the signal. Then, reverse wavelet transformation is utilized to modified wavelet coefficients. Finally, experimental results are given. The results show that block hidden Markov model (BHMM) is a powerful yet simple tool in signal denoising.

Color texture analysis using the wavelet-based hidden Markov model

The wavelet-domain hidden Markov model (WD HMM), in particular the hidden Markov tree (HMT), has recently been proposed and applied to gray texture analysis with encouraging results. For color texture analysis, the previous WD HMM can only be used to model the different color planes individually, assuming they are independent of each other. However, this assumption in general is unrealistic. We show in this paper that the wavelet coefficients have certain inter-dependences between color planes. This paper presents a novel approach to modeling the dependences between color planes as well as the interactions across scales. In our approach, the wavelet coefficients at the same location, scale and sub-band, but different color planes are grouped into one vector. We then propose a multivariate Gaussian mixture model (MGMM) for approximating the marginal distribution of the wavelet coefficient vectors in one scale and capturing the interactions of different color planes. In addition, the statistical dependence between different scales is captured by the transition matrix of the hidden Markov tree. Using this approach, we can improve the performance of the WD HMM on the color texture classification. The experiments show that our WD HMM approach provides 85% of correct classifications (PCC) on 68 color textures from Oulu texture database and outperforms the other wavelet-based methods we study. In this paper, we also investigated the classification performance of the WD HMM methods on different color spaces.

A Robust Multi-Bits Image Watermarking Algorithm Based on HMM in Wavelet Domain

Robustness is an important issue in the development of multi-bits watermarking algorithm. A new algorithm for robust multi-bits image watermarking based on Hidden Markov Model (HMM) in wavelet domain is proposed. The algorithm is characterized as follows: (1) the proposed blind detector based on vector HMM, which is employed to describe the statistics of wavelet coefficients, achieves significant improvements in performance compared to the conventional correlation detector; (2) an adaptive watermark embedding scheme is applied to achieve the low distortion according to the human visual system; (3) an optimal multi-bit watermark embedding strategy and a maximum-likelihood detection for tree structure of vector HMM are proposed through system robustness analysis. Simulation results show that relatively high capacity for watermark embedding in low frequency subbands of wavelet domain is achieved with the proposed algorithm, and high robust results are observed against Stirmark attacks, such as JPEG compress, adding noise, median cut and filter.

Asymmetry of Information Flow between Volatilities Across Time Scales

Conventional time series analysis, focusing exclusively on a time series at a given scale, lacks the ability to explain the nature of the data generating process. A process equation that successfully explains daily price changes, for example, is unable to characterize the nature of hourly price changes. On the other hand, statistical properties of monthly price changes are often not fully covered by a model based on daily price changes. In this paper, we simultaneously model regimes of volatilities at multiple time scales through wavelet-domain hidden Markov models. We establish an important stylized property of volatility across different time scales. We call this property asymmetric vertical dependence. It is asymmetric in the sense that a low volatility state (regime) at a long time horizon is most likely followed by low volatility states at shorter time horizons. On the other hand, a high volatility state at long time horizons does not necessarily imply a high volatility state at shorter time horizons. Our analysis provides evidence that volatility is a mixture of high and low volatility regimes, resulting in a distribution that is non-Gaussian. This result has important implications regarding the scaling behavior of volatility, and consequently, the calculation of risk at different time scales.

Detecting abnormal process trends by wavelet‐domain hidden Markov models

AbstractA novel method for detection of abnormal conditions during plant operation uses wavelet‐domain hidden Markov models (HMMs) as a powerful tool for statistical modeling of wavelet coefficients. By capturing the interdependence of wavelet coefficients of a measured process variable, a classification strategy is developed that can detect abnormal conditions and classify the process behavior on‐line. The method is extended to include multiple measured variables in detection and classification. Two case studies illustrate the potential of this method.

Wavelet-based texture analysis and synthesis using hidden Markov models

Wavelet-domain hidden Markov models (HMMs), in particular, hidden Markov tree (HMT), were recently proposed and applied to image processing, where it was usually assumed that three subbands of the two-dimensional discrete wavelet transform (DWT), i.e., HL, LH, and HH, are independent. In this paper, we study wavelet-based texture analysis and synthesis using HMMs. Particularly, we develop a new HMM, called HMT-3S, for statistical texture characterization in the wavelet domain. In addition to the joint statistics captured by HMT, the new HMT-3S can also exploit the cross correlation across DWT subbands. Meanwhile, HMT-3S can be characterized by using the graphical grouping technique, and has the same tree structure as HMT. The proposed HMT-3S is applied to texture analysis, including classification and segmentation, and texture synthesis with improved performance over HMT. Specifically, for texture classification, we study four wavelet-based methods, and experimental results show that HMT-3S provides the highest percentage of correct classification of over 95% upon a set of 55 Brodatz textures. For texture segmentation, we demonstrate that more accurate texture characterization from HMT-3S allows the significant improvements in terms of both classification accuracy and boundary localization. For texture synthesis, we develop an iterative maximum likelihood-based texture synthesis algorithm which adopts HMT or HMT-3S to impose the joint statistics of the texture DWT, and it is shown that the new RMT-3S enables more visually similar results than HMT does.

Rotation invariant texture characterization and retrieval using steerable wavelet-domain hidden Markov models

We present a statistical model for characterizing texture images based on wavelet-domain hidden Markov models. With a small number of parameters, the new model captures both the subband marginal distributions and the dependencies across scales and orientations of the wavelet descriptors. Applied to the steerable pyramid, once it is trained for an input texture image, the model can be easily steered to characterize that texture at any other orientation. Furthermore, after a diagonalization operation, we obtain a rotation-invariant model of the texture image. We also propose a fast algorithm to approximate the Kullback-Leibler distance between two wavelet-domain hidden Markov models. We demonstrate the effectiveness of the new texture models in retrieval experiments with large image databases, where significant improvements are shown.

Bayesian tree-structured image modeling using wavelet-domain hidden Markov models

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 (e.g., using the expectation-maximization algorithm). We greatly simplify the HMT model by exploiting the inherent self-similarity of real-world images. The simplified model specifies the HMT parameters with just nine meta-parameters (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 new models retain nearly all of the key image 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 visually and in mean square error.