Computational methods for hidden Markov tree models-an application to wavelet trees

The hidden Markov tree models were introduced by Crouse et al. in 1998 for modeling nonindependent, non-Gaussian wavelet transform coefficients. In their paper, they developed the equivalent of the forward-backward algorithm for hidden Markov tree models and called it the "upward-downward algorithm". This algorithm is subject to the same numerical limitations as the forward-backward algorithm for hidden Markov chains (HMCs). In this paper, adapting the ideas of Devijver from 1985, we propose a new "upward-downward" algorithm, which is a true smoothing algorithm and is immune to numerical underflow. Furthermore, we propose a Viterbi-like algorithm for global restoration of the hidden state tree. The contribution of those algorithms as diagnosis tools is illustrated through the modeling of statistical dependencies between wavelet coefficients with a special emphasis on local regularity changes.     

基于隐式马尔科夫参数模型的图像消噪研究

针对隐式马尔科夫模型在图像消噪中的不足,采用参数求解方法.首先对参数模型三元组确定其限制条件,通过递归计算状态概率,通过最大似然估计来使期望最大化,期望最大化过程包括期望过程和最大化过程;在图像消噪中提取观察信号过程利用Kullback-Leibler距离设置其阈值,最终给出了参数解.实验仿真表明本文算法能够保持图像有用信息,执行速度快.     

Adaptive wavelet threshold for image denoising

Threshold selection is the critical issue in image denoising via wavelet shrinkage. Many powerful approaches have been investigated, but few have been to make the threshold values adaptive to the changing statistics of images and meanwhile maintain the efficiency of the algorithm. In this work an efficient adaptive algorithm to capture the dependency of inter-scale wavelet coefficients is proposed. Experiments show that higher peak signal-to-noise ratio can be obtained as compared to other threshold-denoising algorithms.     

基于CHMM 的尖锐频率局部化Contourlet 域图像去噪

提出了一种基于上下文信息隐马尔科夫模型（CHMM）的尖锐频率局部化Contourlet 域图像去噪方法。首先,对噪声图像进行循环平移操作,再利用尖锐频率局部化Contourlet 变换对平移后的图像进行分解,解决了原始Contourlet 变换频率非局部化及缺乏平移不变性的问题,抑制图像在奇异点处产生的伪吉布斯现象。然后,设计一种新的上下文构造方案,针对图像高频子带系数构建CHMM 进行去噪处理。最后,执行尖锐频率局部化Contourlet 逆变换以及逆向循环平移操作获得最终的去噪图像。文中方法采用有效的变换机制并利用上下文信息构建了一个全面的统计相关模型,充分表达了轮廓波高频子带系数在尺度间的持续性、尺度内的多方向选择性和空间邻域内的能量聚集特性,更加有利于图像的去噪处理。实验结果表明:该方法在提高去噪图像PSNR 值的同时进一步改善了其视觉效果,去噪性能优于基于小波变换和原始Contourlet 变换的去噪方法。     

一种新的小波图像去噪方法

小波图像去噪已经成为目前图像去噪的主要方法之一，目前的研究主要集中于如何选取阈值使去噪达到较好的效果。边缘信息是图像最为有用的高频信息，在图像去噪的同时，应尽量保留图像的边缘信息，基于这一思想，提出一种新的小波图像去噪方法。用数学形态学算子对图像小波变换后的小波系数进行处理，以去除具有较小支持域的噪声，保留具有连续支持域的边缘。实验结果表明，与普通的小波阈值去噪方法相比，该方法不但可以保留图像的边缘信息，而且能提高去噪后图像的峰值信噪比2～5dB，提高信噪比6～10dB。     

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.     

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.     

Color monogenic wavelet transform for multichannel image denoising

This paper proposes an effective color image denoising algorithm using the combination color monogenic wavelet transform (CMWT) with a trivariate shrinkage filter. The CMWT coefficients are one order of magnitude with three phases: two phases encode the local color information while the third contains geometric information relating to texture within the color image. In the CMWT domain, a trivariate Gaussian distribution is applied to capture statistical dependencies between the CMWT coefficients, and then a trivariate shrinkage filter is derived using a maximum a posteriori estimator. The performance of the proposed algorithm is experimentally verified using a variety of color test images with a range of noise levels in terms of PSNR and visual quality. The experimental results demonstrate that the proposed algorithm is equal to or better than current state-of-the-art algorithms in both visual and quantitative performance.     

Feature-based wavelet shrinkage algorithm for image denoising.

A selective wavelet shrinkage algorithm for digital image denoising is presented. The performance of this method is an improvement upon other methods proposed in the literature and is algorithmically simple for large computational savings. The improved performance and computational speed of the proposed wavelet shrinkage algorithm is presented and experimentally compared with established methods. The denoising method incorporated in the proposed algorithm involves a two-threshold validation process for real-time selection of wavelet coefficients. The two-threshold criteria selects wavelet coefficients based on their absolute value, spatial regularity, and regularity across multiresolution scales. The proposed algorithm takes image features into consideration in the selection process. Statistically, most images have regular features resulting in connected subband coefficients. Therefore, the resulting subbands of wavelet transformed images in large part do not contain isolated coefficients. In the proposed algorithm, coefficients are selected due to their magnitude, and only a subset of those selected coefficients which exhibit a spatially regular behavior remain for image reconstruction. Therefore, two thresholds are used in the coefficient selection process. The first threshold is used to distinguish coefficients of large magnitude and the second is used to distinguish coefficients of spatial regularity. The performance of the proposed wavelet denoising technique is an improvement upon several other established wavelet denoising techniques, as well as being computationally efficient to facilitate real-time image-processing applications.     

A steerable complex wavelet construction and its application to image denoising.

This work addresses the design of a novel complex steerable wavelet construction, the generation of transform-space feature measurements associated with corner and edge presence and orientation properties, and the application of these measurements directly to image denoising. The decomposition uses pairs of bandpass filters that display symmetry and antisymmetry about a steerable axis of orientation. While the angular characterization of the bandpass filters is similar to those previously described, the radial characteristic is new, as is the manner of constructing the interpolation functions for steering. The complex filters have been engineered into a multirate system, providing a synthesis and analysis subband filtering system with good reconstruction properties. Although the performance of our proposed denoising strategy is currently below that of recently reported state-of-the-art techniques in denoising, it does compare favorably with wavelet coring approaches employing global thresholds and with an "Oracle" shrinkage technique, and presents a very promising avenue for exploring structure-based denoising in the wavelet domain.     

A joint inter- and intrascale statistical model for Bayesian wavelet based image denoising

This paper presents a new wavelet-based image denoising method, which extends a "geometrical" Bayesian framework. The new method combines three criteria for distinguishing supposedly useful coefficients from noise: coefficient magnitudes, their evolution across scales and spatial clustering of large coefficients near image edges. These three criteria are combined in a Bayesian framework. The spatial clustering properties are expressed in a prior model. The statistical properties concerning coefficient magnitudes and their evolution across scales are expressed in a joint conditional model. The three main novelties with respect to related approaches are (1) the interscale-ratios of wavelet coefficients are statistically characterized and different local criteria for distinguishing useful coefficients from noise are evaluated, (2) a joint conditional model is introduced, and (3) a novel anisotropic Markov random field prior model is proposed. The results demonstrate an improved denoising performance over related earlier techniques.     

马尔可夫及隐马尔可夫模型的应用

通过对马尔可夫模型进行深入的分析的基础上对隐马尔科夫模型做了详细的讨论,对马尔科夫模型在语音识别、疾病分析等方面的应用做了介绍,同时针对隐马尔科夫模型在估值问题、解码问题和学习问题等经典问题上的应用做了研究。最后讨论了马尔科夫模型其隐马尔可夫模型的缺陷,并提出相关的改进建议。     

复小波包域复数高斯尺度混合模型图像降噪

提出一种基于四树复小波包变换(QCWPT)复数高斯尺度混合(CGSM)模型的图像去噪新方法。含噪图像经多尺度QCWPT被分解成一个低频复数逼近子图和若干高频复数方向细节子图。在大尺度下,可认为低频逼近子图为信号复系数予以保留;对各尺度复数方向子图按照对数熵代价函数确定最优复小波包基。把能很好刻画小波系数边缘分布形状和局部邻域强相关性的高斯尺度混合(GSM)模型扩展到复小波域,新的CGSM模型具有很好刻画图像幅值和相位信息的能力,并利用该模型对复系数进行贝叶斯最小均方(BLS)估计,从而实现去噪目的。实验结果表明,无论是峰值信噪比(PSNR)指标还是视觉效果,本文方法的去噪性能均好于双树复小波变换(DCWT)、QCWPT和小波域GSM模型去噪,并且在有效去噪的同时,具有很好的图像边缘和细节保护能力。     

Oriented wavelet transform for image compression and denoising.

In this paper, we introduce a new transform for image processing, based on wavelets and the lifting paradigm. The lifting steps of a unidimensional wavelet are applied along a local orientation defined on a quincunx sampling grid. To maximize energy compaction, the orientation minimizing the prediction error is chosen adaptively. A fine-grained multiscale analysis is provided by iterating the decomposition on the low-frequency band. In the context of image compression, the multiresolution orientation map is coded using a quad tree. The rate allocation between the orientation map and wavelet coefficients is jointly optimized in a rate-distortion sense. For image denoising, a Markov model is used to extract the orientations from the noisy image. As long as the map is sufficiently homogeneous, interesting properties of the original wavelet are preserved such as regularity and orthogonality. Perfect reconstruction is ensured by the reversibility of the lifting scheme. The mutual information between the wavelet coefficients is studied and compared to the one observed with a separable wavelet transform. The rate-distortion performance of this new transform is evaluated for image coding using state-of-the-art subband coders. Its performance in a denoising application is also assessed against the performance obtained with other transforms or denoising methods.     

Multivariate statistical modeling for image denoising using wavelet transforms

Recently a variety of efficient image denoising methods using wavelet transforms have been proposed by many researchers. In this paper, we derive the general estimation rule in the wavelet domain to obtain the denoised coefficients from the noisy image based on the multivariate statistical theory. The multivariate distributions of the original clean image can be estimated empirically from a sample image set. We define a parametric multivariate generalized Gaussian distribution (MGGD) model which closely fits the sample distribution. Multivariate model makes it possible to exploit the dependency between the estimated wavelet coefficients and their neighbours or other coefficients in different subbands. Also it can be shown that some of the existing methods based on statistical modeling are subsets of our multivariate approach. Our method could achieve high quality image denoising. Among the existing image denoising methods using the same type of wavelet (Daubechies 8) filter, our results produce the highest peak signal-to-noise ratio (PSNR).     

一种改进的小波阈值裂纹图像去噪法

文中采用一种新的小波阈值法进行数字图像去噪。该方法是在原有小波算法之上进行改进,一方面改进闽值公式,寻求最优的阈值,获取更好的边缘保护,从而达到图像原始信息完整性;另一方面通过优化阁值函数获得改进的阚值方法,提高小波系数阈值判断的准确性,获得更好的去噪效果。实验结果表明,与通常的方法相比较,能更好的去除数字图像噪声、保护图像边缘,获得更好的峰值信噪比、边缘保持指数和更好的视觉效果,达到去噪要求。     

基于自蛇模型和小波分析的图像去噪

提出基于自蛇模型和小波分析的集成图像去噪算法,以及峰值信噪比、保护边缘指数的去噪性能综合评价指标。首先利用自蛇模型对含噪图像滤波,然后将处理后的图像进行小波分解,保持低频分量系数,对其高频分量再次利用自蛇模型去噪,最后对处理后的小波系数进行重构,得到去噪后的图像。实验结果表明,本文算法在去噪能力和和保护边缘能力两方面均好于自蛇模型算法和2次迭代自蛇模型算法。     

Color image denoising with wavelet thresholding based on human visual system model

Recent research in transform-based image denoising has focused on the wavelet transform due to its superior performance over other transform. Performance is often measured solely in terms of PSNR and denoising algorithms are optimized for this quantitative metric. The performance in terms of subjective quality is typically not evaluated. Moreover, human visual system (HVS) is often not incorporated into denoising algorithm. This paper presents a new approach to color image denoising taking into consideration HVS model. The denoising process takes place in the wavelet transform domain. A Contrast Sensitivity Function (CSF) implementation is employed in the subband of wavelet domain based on an invariant single factor weighting and noise masking is adopted in succession. Significant improvement is reported in the experimental results in terms of perceptual error metrics and visual effect.     

基于马尔可夫模型和小波变换的立体残差图像编码

利用立体图像，三维视觉通信能给人提供一种现场真实感。为了产生一个3D系统，必须同时传送两个图像（左图像和右图像）。因此应当研究一种更有效的编码方案。本文首先研究了立体图像的统计特性和左右图像间的交叉相关性，并在分析了视差和残差图像的统计特性后，提出了一个基于小波变换的视差补偿残差（WDCD）的编码方案。仿真实验结果表明，在比特率为0.23bit/pel时，本文的方案重构的残差图像的信噪比（PSNR）和基于DCT的编码方案相比，要高0.58dB。