多小波图像插值算法研究

与单小波变换一样,多小波变换同样具有多分辨分析的特性,1次多小波变换可以将图像分解成4个低频子带和12个高频子带,而且原图像的大小是每个子带的4倍.根据多小波变换的这一特点,利用原图像与经过1次多小波变换后的各高频子带的信息,并考虑各子带的分形维数,提出了一种新颖的灰度图像插值算法.实验结果表明,与传统的插值算法相比,例如双线性插值与双三次多项式插值,该算法的插值效果较好,且克服了单小波插值中出现的斑点干扰.     

基于方向多尺度变换和统计建模的纹理分类方法

纹理是图像分析和识别中经常使用的关键特征, 而小波变换则是图像纹理表示和分类中的常用工具. 然而, 基于小波变换的纹理分类方法常常忽略了小波低频子带信息, 并且无法提取图像纹理的块状奇异信息. 本文提出小波子带系数的局部能量直方图建模方法、轮廓波特征的Poisson 混合模型建模方法和基于轮廓波子带系数聚类的特征提取方法, 并将其应用于图像纹理分类上. 基于局部能量直方图的纹理分类方法解决了小波低频子带的建模难题, 基于Poisson 混合模型的纹理分类方法则首次将Poisson 混合模型用于轮廓子带特征的建模, 而基于轮廓波域聚类的纹理分类方法是一种快速的分类方法. 实验结果显示, 本文所提出的三类方法都超过了当前典型的纹理分类方法.     

一种结合小波模极大值法和Canny算子的目标提取方法

针对基于小波变换的目标提取中忽略低频子图像的一些重要信息的问题.提出了一种基于小波变换的模极大值法和Canny算子的目标提取方法.在小波域中,通过求解局部小波系数模型的极大值点提取(检测)高频边缘,利用Canny算子提取(检测)低频边缘.然后根据融合规则对两个子图像边缘进行融合.实验结果表明,该方法不仅能有效地增强图像边缘,而且能准确地定位图像边缘.     

基于非下采样Contourlet变换与TV模型混合图像去噪算法

在非下采样Contourlet变换的基础上,综合考虑全变差扩散和正态逆高斯模型,提出一种新的图像去噪算法.首先,对图像进行非下采样Contourlet变换,得到高频子带和低频子带系数.然后,对低频子带进行全变差扩散处理,对于方向带通子带,先通过分类准则对其进行分类,将其分为重要系数和不重要系数,对重要系数采样正态逆高斯建模,不重要系数采用高斯分布模型建模.实验结果证明,本文方法在视觉效果、峰值信噪比以及平均结构性上均优于许多算法.     

一种基于二进提升方案的医学图像增强

通过分析和研究二进提升方案,得到一种新的提升二进小波滤波器的构造方法.以新的B-样条二进小波作为初始二进小波滤波器,结合二维6 trous算法对原始医学图像进行多层分解,根据分解后系数特点,一方面对不同级数的高频系数利用单阈值和双阈值函数增强,对低频子带系数用线性拉升来扩大图像的整体对比度.另一方面结合消失矩条件,调整滤波器的提升参数,构造了具有线性相位、紧支撑、高阶消失矩及有限长的单位脉冲响应的提升二进小波,并将其与初始二进小波滤波器增强后图像进行比较.仿真结果表明提升后的滤波器对于对比度低、弱光照图像比初始滤波器的增强效果有了进一步提高,噪声放大问题有明显改善,更好地突出图像边缘特征、保留了图像更多细节信息.     

用于JPEG2000图像认证的鲁棒性水印算法

针对JPEG2000图像压缩标准所具有的渐进传输、一次编码多次解码等特性,提出了一种基于图像特征的鲁棒性图像认证算法.该算法在JPEG2000编码过程中,先根据图像不变特征,生成认证水印,再根据实际的鲁棒性认证需求,在量化后的小波系数中确定每个子带的认证水印嵌入位平面,最后基于小波系数位平面的特征嵌入认证水印.算法不仅能适应JPEG2000各种灵活的编码方式,还能定位图像篡改的位置.实验结果验证了图像认证算法对可允许图像操作的鲁棒性以及对图像篡改的敏感性.     

基于多尺度几何分解的光照不均图像增强方法

针对光照不均匀的图像,结合W系统和NSCT变换,提出了一种新的图像增强方法.方法首先利用W变换对图像进行多尺度分解,然后利用NSCT中的非下采样方向滤波器组对尺度分解中的高频部分进行方向分解,得到不同尺度不同方向上的变换系数.在多尺度几何分解的基础上,对低频子带图像采用动态直方图均衡化、高频子带图像采用同态滤波的方法进行增强处理,最后利用非线性函数减小图像明、暗部分灰度值的差异,得到最后的增强结果.仿真实验结果表明,算法无论在视觉效果上还是客观评价指标上都优于其他被比较的四种增强算法,对于过亮、过暗以及局部光照不均匀的图像均取得了更好的增强效果,在增强图像细节的同时能有效抑制图像的伪吉布斯失真和过增强失真.在评价指标上,算法对三组经典图像处理后的增强图像的信息熵分别达到了10.0755、9.7879、10.5338,明显优于其他方法.     

正交小波包及其在数字信号压缩中的应用

正交小波包是正交多分辨分析构造正交小波思想的自然延伸,正交小波包变换可以进一步分割小波空间,解决小波变换“高频低分辨”的问题,为数字信号处理提供获得高频高分辨效果的分析工具。最后,将小波包分析用于数字信号压缩问题的研究,获得了很好的变换压缩效果     

适应于图像压缩的11/9小波基构造

根据正交多分辨分析理论,利用求解低通和高通滤波的系数,可构造出多种正交小波.但正交小波中只有Haar小波满足对称性,这不适合在图像处理方面的应用.在提升格式的小波变换出现之前,小波分解通过Mallat算法来完成,而提升格式的小波有显著的优点,运算量少,不同小波运算量减少程度不一样,一般减少在25%到50%之间.文章根据双正交对称紧支集小波的消失矩、对称性、短支撑等一系列条件和其他构造原理,构造出一个适应图像压缩的11/9双正交提升小波,并满足Cohen-Daubechies准则.同时,为了便于小波变换的硬件实现,最佳的状态是,分解和重构滤波系数为二进制分数,且根据不同参数取值,让子带编码增益G_(SBC)达到最大.     

基于Curvelet变换的数字水印算法

数字水印技术能起到版权保护的作用,从数字水印的鲁棒性与不可感知性要求出发,介绍了Curvelet变换的多方向、多分辨、带通特点及各层的系数特征,提出了一种基于Curvelet变换和HVS的图像数字水印技术,这种数字水印方法是将数字水印嵌入到原始图像经Curvelet变换后的高频系数构成的矩阵当中.仿真实验表明该算法简单有效,原图像与嵌入水印后图像差异小,水印提取准确,不仅能保证数字水印不可感知性,而且在对嵌入水印图像进行裁剪、加噪、旋转及涂改等攻击后具有较强的鲁棒性.     

Digital watermarking scheme for colour remote sensing image based on quaternion wavelet transform and tensor decomposition

Digital watermarking is important for protecting the intellectual property of remote sensing images. Unlike watermarking in ordinary colour images, in colour remote sensing images, watermarking has an important requirement: robustness. In this paper, a robust nonblind watermarking scheme for colour remote sensing images, which considers both frequency and statistical pattern features, is constructed based on the quaternion wavelet transform (QWT) and tensor decomposition. Using the QWT, not only the abundant phase information can be used to preserve detailed host image features to improve the imperceptibility of the watermark, but also the frequency coefficients of the host image can provide a stable position to embed the watermark. To further strengthen the robustness, the global statistical feature structure acquired through the tensor Tucker decomposition is employed to distribute the watermark's energy among different colour bands. Because both the QWT frequency coefficients and the tensor decomposition global statistical feature structure are highly stable against external distortion, their integration yields the proposed scheme, which is robust to many image manipulations. A simulation experiment shows that our method can balance the trade‐off between imperceptibility and robustness and that it is more robust than the traditional QWT and discrete wavelet transform (DWT) methods under many different types of image manipulations.     

基于小波多分辨率分析和改进窄带法的C-V水平集图像分割模型

本文研究了基于小波分析改进的C-V模型图像分割问题.利用小波多分辨率分析和改进的窄带水平集方法,获得了比传统C-V模型分割速度更快、准确度更高、算法复杂度更低的分割结果.推广了C-V水平集模型如何快速准确地分割灰度不均匀的图像和窄带水平集法等结果.     

Main frequency band of blast vibration signal based on wavelet packet transform

As a key parameter in blasting safety criteria, accurately describing the frequency's characteristics is of practical significance. Due to the deficiency of Fourier transform in the analysis of non-periodic and non-stationary signals, this study defined a wavelet frequency domain parameter, referred to as a main frequency band. A computational method associated with the wavelet packet transform is also proposed. To verify the feasibility of main frequency band and the proposed computational method in describing blasting frequency characteristics, an application is exemplified with field blasting vibration signals monitored in a mine. The effects of explosive charge and distance on main frequency band distribution characteristics are also studied. Results show that the main frequency band based on the computational method is a sensitive, accurate and efficient frequency parameter; it can accurately describe the frequency characteristics of blasting signals and effectively overcome the drawbacks in Fourier transform. When the explosive charge is constant, the span of main frequency reduces as a whole as the distance increases, and the frequency domain energy of blast vibration signals are concentrated mainly in the low-frequency range. When the distance is constant, the peak energy of blast vibration signals increase with the increase of explosive charge, without obvious change in main frequency band. To avoid the effects of interferences on frequency characteristics, the least square method is employed to eliminate signal trend components, and the wavelet threshold method with a hard thresholding function and the Birge–Massart strategy is applied in denoising.     

Contrast enhancement for image by WNN and GA combining PSNR with information entropy

A new contrast enhancement algorithm for image is proposed combining genetic algorithm (GA) with wavelet neural network (WNN). In-complete Beta transform (IBT) is used to obtain non-linear gray transform curve so as to enhance global contrast for an image. GA determines optimal gray transform parameters. In order to avoid the expensive time for traditional contrast enhancement algorithms, which search optimal gray transform parameters in the whole parameters space, based on gray distribution of an image, a classification criterion is proposed. Contrast type for original image is determined by the new criterion. Parameters space is, respectively, determined according to different contrast types, which greatly shrink parameters space. Thus searching direction of GA is guided by the new parameter space. Considering the drawback of traditional histogram equalization that it reduces the information and enlarges noise and background blur in the processed image, a synthetic objective function is used as fitness function of GA combining peak signal-noise-ratio (PSNR) and information entropy. In order to calculate IBT in the whole image, WNN is used to approximate the IBT. In order to enhance the local contrast for image, discrete stationary wavelet transform (DSWT) is used to enhance detail in an image. Having implemented DSWT to an image, detail is enhanced by a non-linear operator in three high frequency sub-bands. The coefficients in the low frequency sub-bands are set as zero. Final enhanced image is obtained by adding the global enhanced image with the local enhanced image. Experimental results show that the new algorithm is able to well enhance the global and local contrast for image while keeping the noise and background blur from being greatly enlarged.     

Average densities of frequency bands of wavelets

A function is called a wavelet if its integral translations and dyadic dilations form an orthonormal basis for L ²(?). The support of the Fourier transform of a wavelet is called its frequency band. In this paper, we study the relation between diameters and measures of frequency bands of wavelets, precisely say, we study the ratio of the measure to the diameter. This reflects the average density of the frequency band of a wavelet. In particular, for multiresolution analysis (MRA) wavelets, we do further research. First, we discuss the relation between diameters and measures of frequency bands of scaling functions. Next, we discuss the relation between frequency bands of wavelets and the corresponding scaling functions. Finally, we give the precise estimate of the measure of frequency bands of wavelets. At the same time, we find that when the diameters of frequency bands tend to infinity, the average densities tend to zero.     

A METHOD TO APPROACH OPTIMAL RESTORATION IN IMAGE RESTORATION PROBLEMS WITHOUT NOISE ENERGY INFORMATION

This paper proposes a new image restoration technique, in which the resulting regularized image approximates the optimal solution steadily. The affect of the regular-ization operator and parameter on the lower band and upper band energy of the residue of the regularized image is theoretically analyzed by employing wavelet transform. This paper shows that regularization operator should generally be lowstop and highpass. So this paper chooses a lowstop and highpass operator as regularization operator, and construct an optimization model which minimizes the mean squares residue of regularized solution to determine regularization parameter. Although the model is random, on the condition of this paper, it can be solved and yields regularization parameter and regularized solu-tion. Otherwise, the technique has a mechanism to predict noise energy. So, without noisei nformation, it can also work and yield good restoration results.     

基于多小波变换提高地震数据的分辨率

给出了设计接近地震子波的小波函数方法,使得地震信号的小波分解能量相对集中,有利于做各种处理;通过选出最匹配子波的的小波函数,做多小波变换;利用分频处理函数来补偿石油勘探中地震数据中损失的高频成分,以提高石油勘探中地震数据分辨率.通过对反射信号的高频成分进行补偿,可使地震剖面的主频得到很大提高,频宽得到扩展,可获得较高分辨率的地震剖面.从实际数据处理结果可以看出,方法是可行的且是有效的.     

Wavelet Shrinkage on Paths for Denoising of Scattered Data

We propose a new algorithm for denoising of multivariate function values given at scattered points in ${\mathbb{R}^{d}}$ . The method is based on the one-dimensional wavelet transform that is applied along suitably chosen path vectors at each transform level. The idea can be seen as a generalization of the relaxed easy path wavelet transform by Plonka (Multiscale Model Simul 7:1474–1496, 2009) to the case of multivariate scattered data. The choice of the path vectors is crucial for the success of the algorithm. We propose two adaptive path constructions that take the distribution of the scattered points as well as the corresponding function values into account. Further, we present some theoretical results on the wavelet transform along path vectors in order to indicate that the wavelet shrinkage along path vectors can really remove noise. The numerical results show the efficiency of the proposed denoising method.