Dual-tree complex wavelet hidden Markov tree model for image denoising

A new non-training complex wavelet hidden Markov tree (HMT) model, which is based on the dual-tree complex wavelet transform and a fast parameter estimation technique, is proposed for image denoising. This new model can mitigate the two problems (high computational cost and shift-variance) of the conventional wavelet HMT model simultaneously. Experiments show that the denoising approach with this new model achieves better performance than other related HMT- based image denoising algorithms.     

用于SAR图像分割的第二代Bandelet域HMT-3S模型

针对传统的基于变换域隐马尔可夫树(Hidden Markov Tree,HMT)模型的SAR图像分割方法不能得到较满意的区域一致性结果和较准确的分割边缘的问题,提出了一种基于第二代Bandelet域HMT-3S模型的SAR图像分割方法(BHMT-3Sseg).HMT-3S模型是一种融合了子带间相关性的HMT模型,在描述图像纹理特征时,更具合理性.BHMT-3Sseg方法采用HMT-3S模型对图像的第二代Bandelet系数建模,通过HMT-3S模型参数的训练、各尺度似然值的计算和基于邻域背景的多尺度融合,实现对SAR图像的分割,既能得到较为准确和连续的边缘,也增强了分割结果的区域一致性.实验表明,本文方法BHMT-3Sseg对SAR图像分割是可行有效的.     

Bayesian tree-structured image modeling using wavelet-domain hiddenMarkov 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.     

基于小波域隐马尔可夫混合模型的SAR图像降斑算法

在小波域马尔可夫随机场(MRF)和隐马尔可夫树(HMT)的基础上,提出了一种新的合成孔径雷达(SAR)图像降斑算法.该算法在对乘性噪声不取对数变换的情况下,融合了贝叶斯最小均方误差(MMSE)抑制噪声技术.为了提高HMT的速度,采用了一个新的隐马尔可夫半树模型,该模型考虑了小波系数的持续性和聚类性,分别用HMT和MRF刻画.仿真结果表明该算法在抑制斑点噪声的同时,有效的保持了边缘,避免对数变换带来的一些误差,取得了好的效果,其速度比HMT模型提高了二十倍.     

Directional multiscale modeling of images using the contourlet transform.

The contourlet transform is a new two-dimensional extension of the wavelet transform using multiscale and directional filter banks. The contourlet expansion is composed of basis images oriented at various directions in multiple scales, with flexible aspect ratios. Given this rich set of basis images, the contourlet transform effectively captures smooth contours that are the dominant feature in natural images. We begin with a detailed study on the statistics of the contourlet coefficients of natural images: using histograms to estimate the marginal and joint distributions and mutual information to measure the dependencies between coefficients. This study reveals the highly non-Gaussian marginal statistics and strong interlocation, interscale, and interdirection dependencies of contourlet coefficients. We also find that conditioned on the magnitudes of their generalized neighborhood coefficients, contourlet coefficients can be approximately modeled as Gaussian random variables. Based on these findings, we model contourlet coefficients using a hidden Markov tree (HMT) model with Gaussian mixtures that can capture all interscale, interdirection, and interlocation dependencies. We present experimental results using this model in image denoising and texture retrieval applications. In denoising, the contourlet HMT outperforms other wavelet methods in terms of visual quality, especially around edges. In texture retrieval, it shows improvements in performance for various oriented textures.     

基于小波域多状态隐马尔科夫树模型的自适应文本图像分割算法

本文针对文本图像首先提出了一种基于小波域多状态隐马尔科夫树模型的自适应文本图像分割算法(Context-Adapted wavelet-domain Hidden Markov Tree,简称为CAHMT),该算法具有较高的分割质量和较低的计算复杂度.其次,为了进一步提高CAHMT算法分割的效果,将该算法与微分算子、尺度系数相结合提出了两种新的文本图像分割算法.最后通过实例阐明了这些算法的有效性.     

基于小波变换及隐式马尔科夫树模型的图像信号去噪

研究基于小波变换的隐式马尔科夫模型树(HMT)方法,用于去除图像信号中的白噪声。该方法利用了小波变换域系数间的相关性和自相似信息,并在Lenna图像中验证了方法的有效性。对不同程度污染的高斯白噪声图像的去噪效果与传统方法进行比较;结果表明,基于小波变换的HMT方法有更好的去噪效果,所建立的HMT模型更能体现图像的特征。     

改进的contourlet变换域隐马尔可夫树模型

Contourlet域隐马尔科夫树(C_HMT)模型不但可以描述尺度间的相关性,而且可以对方向子带间contourlet系数的相关性做出统计描述,是一种比小波域HMT模型更为有效的系数相关性描述方法.本文提出了一种改进的contourlet变换域HMT模型,节点的状态不只依赖于其父节点的状态,而且兼顾到其父节点相邻节点的状态.这种模型可以进一步捕捉尺度间contourlet变换系数更为丰富的相关性,从而能够更准确和有效的刻画contourlet变换系数的非高斯性和持续性.将该模型应用于图像的去噪,并与另外几种典型的去噪算法作定性比较,验证了本文提出的改进的C_HMT模型在图像去噪性能方面有一定的优越性.     

Wavelet-based statistical signal processing using hidden Markovmodels

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. We develop a new framework for statistical signal processing based on wavelet-domain hidden Markov models (HMMs) that concisely models the statistical dependencies and non-Gaussian statistics encountered in real-world signals. Wavelet-domain HMMs 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 HMMs 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 HMMs, we develop novel algorithms for signal denoising, classification, and detection     

基于Contourlet域HMT-3S模型的激光主动成像图像分割

基于Contourlet系数分布统计特性,结合隐马尔科夫树(HMT)-3S模型和贝叶斯准则,提出了一种基于Contourlet域HMT-3S模型的图像分割算法(CHMT-3Sseg),并将其用于激光主动成像图像的分割。CHMT-3Sseg方法首先利用HMT-3S模型充分挖掘子带间的相关性,通过HMT-3S模型参数训练和似然值计算得到了可靠的初始分割。为了获得较好的区域一致性和边缘准确性,对初始分割结果进行了基于邻域背景的多尺度融合。对合成图像和激光主动成像图像的实验结果表明:CHMT-3Sseg不但在边缘和方向信息保持上有明显改进,而且错分概率显著降低,对真实图像得到了理想的分割效果。     

Multiscale image segmentation using wavelet-domain hidden Markovmodels

We introduce a new image texture segmentation algorithm, HMTseg, based on wavelets and the hidden Markov tree (HMT) model. The HMT is a tree-structured 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 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 wavelet-compressed images without the need for decompression into the space domain. We demonstrate the performance of HMTseg with synthetic, aerial photo, and document image segmentations.     

复小波域HMT模型图像复原

提出了基于二元树复小波变换（DT-CWT）的复小波域隐马尔可夫树（HMT）模型线性图像复原算法,并采用一种简单可行的快速算法来估计HMT模型参数。该方法较好地再现了各种边缘信息,其复原结果较传统的复原方法有不同程度的提高,其运行效率较传统的HMT模型参数估计方法有明显的提高。     

基于小波域多状态隐马尔科夫树模型多尺度文本图像分割

该文基于小波域多状态隐马尔科夫树（HMT）模型，引入一种新的文本分割方法。该分割方法是在H.Choi et al.(2001)工作的基础上，将文本按纹理分为背景、文字与图片3种类型，分别建立多状态HMT模型。另外，基于平滑图像将上述方法又作了进一步的改进，引入了多状态IHMT分割方法，最后通过实例阐明了方法的有效性。     

Contourlet domain locally optimum image watermark decoder using Cauchy mixtures based vector HMT model

Digital image watermarking has become a necessity in many applications such as data authentication, broadcast monitoring on the Internet and ownership identification. Various watermarking schemes have been proposed to protect the copyright information. There are three indispensable, yet contrasting requirements for a watermarking scheme: imperceptibility, robustness and payload. Therefore, a watermarking scheme should provide a trade-off among these requirements from the information-theoretic perspective. Generally, in order to enhance the imperceptibility, robustness and payload simultaneously, the human visual system (HVS) and the statistical properties of the image signal should be fully taken into account. The statistical model-based transform domain multiplicative watermarking scheme embodies the above ideas, and therefore the detection and extraction of the multiplicative watermarks have received a great deal of attention. The performance of a statistical model-based watermark detector or decoder is highly influenced by the accuracy of the statistical model itself and the applicability of decision rule. In this paper, we firstly propose a new hidden Markov trees (HMT) statistical model in Contourlet domain, namely Cauchy mixtures-based vector HMT (vector CMM–HMT), by describing the marginal distribution with Cauchy mixture model (CMM) and grouping Contourlet coefficients into a vector, which can capture both the subband marginal distributions and the strong dependencies across scales and orientations of the Contourlet coefficients. Then, by modeling the Contourlet coefficients with vector CMM–HMT and employing locally most powerful (LMP) test, we develop a locally optimum image watermark decoder in Contourlet domain. We conduct extensive experiments to evaluate the performance of the proposed blind watermark decoder, in which encouraging results validate the effectiveness of the proposed technique, in comparison with the state-of-the-art approaches recently proposed in the literature.     

Removal of Correlated Noise by Modeling the Signal of Interest in the Wavelet Domain

Images, captured with digital imaging devices, often contain noise. In literature, many algorithms exist for the removal of white uncorrelated noise, but they usually fail when applied to images with correlated noise. In this paper, we design a new denoising method for the removal of correlated noise, by modeling the significance of the noise-free wavelet coefficients in a local window using a new significance measure that defines the “signal of interest” and that is applicable to correlated noise. We combine the intrascale model with a hidden Markov tree model to capture the interscale dependencies between the wavelet coefficients. We propose a denoising method based on the combined model and a less redundant wavelet transform. We present results that show that the new method performs as well as the state-of-the-art wavelet-based methods, while having a lower computational complexity.      

基于独立混合模型的EM算法参数初始化实现方法

隐马尔科夫树( Hidden Markov Tree, HMT )的状态不能被观测到,只能观测到另一个与状态有联系的量,通过观测量估计HMT模型参数是一个不完全数据参数估计问题。期望最大化( Expectation Maximization, EM )算法是一种求参数极大似然估计的迭代算法,可以用于解决不完全数据参数估计问题,因此被广泛应用于HMT模型的参数估计中。当初始参数偏离真实参数较大时,EM算法迭代次数多,收敛速度慢,通过一个计算量不大的参数初始化处理,能够有效减少EM算法的迭代次数,加快收敛速度。本文提出了一种基于独立混合模型的参数初始化方法,详细介绍了该方法的实现过程,通过采用独立混合模型进行参数初始化,使得EM算法的迭代次数明显减少,收敛速度大大提高。最后,计算机仿真验证了该方法的可行性和有效性。      

HMT与HMRF联合的SAR图像小波去斑方法

该文将隐马尔可夫树(HMT)和隐马尔可夫随机场(HMRF)两种模型相结合,提出了一种新的估计SAR图像小波系数隐状态的迭代算法.使用该算法可以充分利用小波系数尺度间和尺度内的相关性,更准确地估计隐状态.在此基础上,通过贝叶斯估计分离出小波系数中的信号成分即可消除噪声影响.实验结果表明,该算法能够有效抑制SAR图像相干斑,同时可较好地保持边缘等图像结构特征.     

Varying complexity in tree-structured image distribution models.

Probabilistic models of image statistics underlie many approaches in image analysis and processing. An important class of such models have variables whose dependency graph is a tree. If the hidden variables take values on a finite set, most computations with the model can be performed exactly, including the likelihood calculation, training with the EM algorithm, etc. Crouse et al. developed one such model, the hidden Markov tree (HMT). They took particular care to limit the complexity of their model. We argue that it is beneficial to allow more complex tree-structured models, describe the use of information theoretic penalties to choose the model complexity, and present experimental results to support these proposals. For these experiments, we use what we call the hierarchical image probability (HIP) model. The differences between the HIP and the HMT models include the use of multivariate Gaussians to model the distributions of local vectors of wavelet coefficients and the use of different numbers of hidden states at each resolution. We demonstrate the broad utility of image distributions by applying the HIP model to classification, synthesis, and compression, across a variety of image types, namely, electrooptical, synthetic aperture radar, and mammograms (digitized X-rays). In all cases, we compare with the HMT.     

A mixed MAP/MLSE receiver for convolutional coded signalstransmitted over a fading channel

This paper addresses the problem of estimating a rapidly fading convolutionally coded signal such as might be found in a wireless telephony or data network. We model both the channel gain and the convolutionally coded signal as Markov processes and, thus, the noisy received signal as a hidden Markov process (HMP). Two now-classical methods for estimating finite-state hidden Markov processes are the Viterbi (1967) algorithm and the a posteriori probability (APP) filter. A hybrid recursive estimation procedure is derived whereby one hidden process (the encoder state in our application) is estimated using a Viterbi-type (i.e., sequence based) cost and the other (the fading process) using an APP-based cost such as maximum a posteriori probability. The paper presents the new algorithm as applied specifically to this problem but also formulates the problem in a more general setting. The algorithm is derived in this general setting using reference probability methods. Using simulations, performance of the optimal scheme is compared with a number of suboptimal techniques-decision-directed Kalman and HMP predictors and Kalman filter and HMP filter per-survivor processing techniques     

Hidden Markov models for wavelet-based blind source separation.

In this paper, we consider the problem of blind source separation in the wavelet domain. We propose a Bayesian estimation framework for the problem where different models of the wavelet coefficients are considered: the independent Gaussian mixture model, the hidden Markov tree model, and the contextual hidden Markov field model. For each of the three models, we give expressions of the posterior laws and propose appropriate Markov chain Monte Carlo algorithms in order to perform unsupervised joint blind separation of the sources and estimation of the mixing matrix and hyper parameters of the problem. Indeed, in order to achieve an efficient joint separation and denoising procedures in the case of high noise level in the data, a slight modification of the exposed models is presented: the Bernoulli-Gaussian mixture model, which is equivalent to a hard thresholding rule in denoising problems. A number of simulations are presented in order to highlight the performances of the aforementioned approach: 1) in both high and low signal-to-noise ratios and 2) comparing the results with respect to the choice of the wavelet basis decomposition.