双密度双树复小波域多聚焦图像融合

将双密度双树复小波变换引入多分辨率图像融合中,利用双密度双树复小波变换的多尺度、多方向性和平移不变性特征分解多聚焦图像,对分解后高、低频图像系数采用不同融合策略进行融合,应用双密度双树复小波逆变换重构图像。采用多组多焦距源图像进行融合实验,并对融合结果进行了客观评价。实验结果表明双密度双树复小波域融合方法对多聚焦图像具有更好的融合效果,图像的细节描述更加精确。     

一种图像增强新方法

提出了一种四树复小波包变换域层内层间系数相关性图像增强新方法。该方法利用四树复小波包变换具有移不变性、良好方向选择性和对高频信号的细致分析能力,把含噪图像分解成低频逼近子图和若干高频方向子图;在保留低频逼近子图复系数不变的同时,充分利用变换域信号复系数层间相关性强和噪声复系数层间相关性弱的特点,采用非高斯双变量模型对每一个方向子图复系数进行降噪处理。同时考虑图像的弱边缘在变换域某些方向子图内复系数值较大,而在其他方向子带内其值较小的特点,甄别出弱边缘点对应的复系数并进行增强处理。实验结果表明,无论是PSNR指标,还是在视觉效果上,该方法的增强性能均好于传统的双树复小波变换去噪、四树复小波包变换去噪和小波域高斯尺度混合模型去噪,在有效抑制噪声的同时,具有很好的图像弱边缘增强和细节保护能力。     

一种有效保留图像细节的自适应图像消噪方法

针对更多保留图像细节信息有效滤除噪声的问题,分析了双密度双树复小波的变换原理及特点,推导了双变量萎缩函数,提出一种基于双密度双树复小波变换的局域自适应图像消噪算法。首先对含噪图像进行双密度双树复小波分解;后根据小波系数的统计特性以及层内和层间系数的相关性,采用结合局域方差估计的双变量萎缩函数对小波系数进行处理,并用处理后的小波系数重构图像。实验结果表明：该算法在滤除噪声的同时可保留更多的图像细节,极大地改善了图像的视觉质量。     

双树复小波域的邻域自适应贝叶斯收缩去噪

为了更加高效去除图像采集或传输中引入的噪声,提出了一种基于双树复小波域的邻域自适应贝叶斯收缩的图像去噪方法,利用了双树复小波变换的平移不变性和更多的方向选择性的优点,并考虑了系数间的局部自适应邻域相关性,以尺度适合的窗口为单位估计相应系数的方差,利用滑窗求其平均作为整个子带的图像方差,通过贝叶斯收缩来处理小波系数,从而实现高效的图像去噪。实验结果证明,该方法取得了很高的峰值信噪比和更好的视觉效果,去噪性能优良。     

基于混合小波变换的医学超声图像自适应去斑

针对小波去斑方法在医学超声图像抑斑上的不足,提出一种混合离散小波变换DWT(Discrete Wavelet Transform)和双树复小波变换DTCWT(Dual-tree Complex Wavelet Transform)进行阈值处理和变量收缩的医学超声图像自适应去斑算法。首先,在小波域,根据小波系数能量的特点,计算综合阈值实现图像预处理;然后,结合小波系数的尺度相关性,提出一种改进的三变量收缩函数,实现图像去斑。实验结果表明该方法较已有的经典方法更为有效,一般情况信噪比可提高0.6~2.6dB,图像边缘信息保持能力更突出。     

一种基于双树复小波变换的图像融合方法

提出了一种基于双树复小波变换的图像融合方法。采用双树复小波变换对源图像进行分解后,该方法首先对各频域分别定义一种活性测度和匹配测度,再通过相应的匹配测度来计算各频域的融合因子,然后采用加权与选择相结合的规则融合高频系数和低频系数,得到融合图像的各频域系数。最后,采用双树复小波逆变换重构得到融合图像。实验表明,该融合方法具有良好的客观评价性能和主观视觉效果。     

基于双树复小波域的马尔可夫随机场样本修补算法

为了消除大目标图像修补过程中,修补区域由于累积误差引起的马赛克和振铃效应,提出基于双树复小波域的马尔可夫随机场(MRF)样本修补算法。首先应用双树复小波变换(DTCWT)将待修补图像变换到复频域,通过合理的置信度和数据项计算待修补块的修补顺序;然后应用MRF样本修补算法在不同尺度、不同方向下修补未知区域;最后利用双树复小波逆变换重构图像。实验结果表明,与传统离散小波修补方法相比,双树复小波域MRF样本修补算法能更好地保持修补区域纹理和结构信息。     

小波域多方向信息融合的纹理图像检索

由于能提供较多的方向信息,双树复小波变换在纹理图像检索中的检索率高于传统小波变换,但传统小波变换与双树复小波变换得到的方向子带不同。针对该问题,提出一种融合传统小波和双树复小波变换的一阶统计信息从而提取特征进行纹理图像检索的方法。对Brodatz图像库的仿真实验表明,该方法优于传统小波和双树复小波方法。     

基于双树复小波的图像修复

小波变换技术已被广泛应用于图像修复领域,但其在图像修复过程中出现的边缘部分模糊或不连接的情况成为了一个难点。针对此问题,提出了基于双树复小波变换的图像修复算法。该算法使用双树复小波变换对破损图像进行多尺度和多方向的分解,对各个高频方向子带使用全变分(Total Variation,TV)模型进行快速修复,各个低频分量使用改进了的曲率驱动扩散(Curvature-Driven-Diffusions,CCD)模型进行迭代修复,最后通过小波逆变换得到最终的修复图像。实验结果表明,该方法很好地推广了双树复小波变换在图像修复领域中的应用,并且在图像纹理的修复以及在结构部分的填充都有较好的效果。     

复小波包变换域混合统计模型图像降噪算法

该方法利用四树复小波包变换具有的移不变性、良好的方向选择性和对高频信号的细致分析能力等特点, 把含噪图像分解成低频逼近子图和若干高频方向子图; 在保留低频逼近子图复系数不变的同时, 利用复系数层间相关性的强弱把高频方向子图分为主要类和次要类. 对主要类和次要类复系数分别进一步采用非高斯双变量模型和零均值高斯分布模型进行噪声抑制. 实验结果表明, 无论是峰值信噪比(PSNR)指标, 还是在视觉效果上, 本文方 法的去噪性能均好于传统的双树复小波变换去噪、四树复小波包变换去噪和小波域高斯尺度混合模型去噪, 在有效抑制噪声的同时, 具有很好的图像边缘和细节保护能力.     

基于小波系数关系的图像去噪方法

为了在保留图像边缘信息的同时,尽可能地去除图像噪声,提出一种基于小波系数尺度间和尺度内关系的去噪方法。该方法使用小波系数的相关系数和邻域小波系数的平均幅值来分别表示小波系数的尺度间和尺度内关系,并以此来辨别出图像的边缘信息和噪声;同时提出了一种阈值函数来处理图像的小波系数。实验表明该方法能取得较高的信噪比,并能保存图像的一些细节信息。     

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.     

On the statistical decorrelation of the 2D discrete wavelet transform coefficients of a wide sense stationary bivariate random process

We present a second order statistical analysis of the 2D Discrete Wavelet Transform (2D DWT) coefficients. The input images are considered as wide sense bivariate random processes. We derive closed form expressions for the wavelet coefficientsʼ correlation functions in all possible scenarios: inter-scale and inter-band, inter-scale and intra-band, intra-scale and inter-band and intra-scale and intra-band. The particularization of the input process to the White Gaussian Noise (WGN) case is considered as well. A special attention is paid to the asymptotical analysis obtained by considering an infinite number of decomposition levels. Simulation results are also reported, confirming the theoretical results obtained. The equations derived, and especially the inter-scale and intra-band dependency of the 2D DWT coefficients, are useful for the design of different signal processing systems as for example image denoising algorithms. We show how to apply our theoretical results for designing state of the art denoising systems which exploit the 2D DWT.     

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.     

A new wavelet-based fuzzy single and multi-channel image denoising

In this paper, we propose a new wavelet shrinkage algorithm based on fuzzy logic. In particular, intra-scale dependency within wavelet coefficients is modeled using a fuzzy feature. This feature space distinguishes between important coefficients, which belong to image discontinuity and noisy coefficients. We use this fuzzy feature for enhancing wavelet coefficients' information in the shrinkage step. Then a fuzzy membership function shrinks wavelet coefficients based on the fuzzy feature. In addition, we extend our noise reduction algorithm for multi-channel images. We use inter-relation between different channels as a fuzzy feature for improving the denoising performance compared to denoising each channel, separately. We examine our image denoising algorithm in the dual-tree discrete wavelet transform, which is the new shiftable and modified version of discrete wavelet transform. Extensive comparisons with the state-of-the-art image denoising algorithm indicate that our image denoising algorithm has a better performance in noise suppression and edge preservation.     

Hybrid inter- and intra-wavelet scale image restoration

This paper exploits both the inter- and intra-scale interdependencies that exist in wavelet coefficients to improve image restoration from noise-corrupted data. Using an over-complete wavelet expansion, we group the wavelet coefficients with the same spatial orientation at several scales. We then apply the linear minimum mean squared-error estimation to smooth noise. This scheme exploits the inter-scale correlation information of wavelet coefficients. To exploit the intra-scale dependencies, we calculate the co-variance matrix of each vector locally using a centered square-shaped window. Experiments show that the proposed hybrid scheme significantly outperforms methods exploiting only the intra- or inter-scale dependencies. The performance of noise removal also depends on wavelet filters. In our experiments a biorthogonal wavelet, which best characterizes the image inter-scale dependencies, achieves the best results.     

改进阈值与尺度间相关的小波红外图像去噪

为了更有效地去除红外图像中的噪声, 提出一种基于改进阈值与尺度间相关的小波红外图像去噪方法. 一方面利用阈值修正方案和新阈值函数对通常的小波阈值去噪法进行改进; 另一方面通过对阈值邻近的小波系数进行小波变换尺度间相关性估计, 提高小波系数阈值判断的准确性.实验结果表明, 与通常的小波阈值去噪法相比,该算法能更有效地去除红外图像中的噪声, 获得更高的峰值信噪比(Peak signal-to-noise ratio, PSNR)、边缘保持指数(Edge preserved index, EPI)和更好的视觉效果,具有较好的实用性.     

PDTDFB变换和双变量模型在图像去噪中的应用

对金字塔复方向滤波器组和贝叶斯最大后验估计理论架构下的双变量模型进行研究的基础上,结合二者的优点,提出一种新的图像去噪算法。PDTDFB（Pyramidal Dual-Tree Directional Filter Bank）变换具有近似时移不变性、多尺度、多方向选择性好的特点;双变量模型充分突出图像分解后系数的尺度内和尺度间的双重相关性;对噪声估计方法做出了详细阐述。仿真实验表明,与已有的多尺度理论（如：轮廓波等）和一些典型的图像去噪算法相比较,该算法的客观评价指标PSNR以及去噪后图像的主观视觉效果都有明显的提高和改善,能有效地保留原始图像的纹理和细节信息。