Haar小波滤波器序列只有两个非零项的论证

Haar小波是最简单的紧支集正交小波（Daubechies小波）,其滤波器序列较短,在图像处理等诸多领域都有广泛的应用。由Daubechies小波的构造理论可知,现有的正交小波是在比较特殊的前提下得到的,则Haar小波的滤波器系数序列的唯一确定性受到质疑。以多分辨分析为基础,在时域对Haar小波滤波器系数序列的唯一性进行了论证,即证明了Haar小波滤波器序列只有两个非零项,这对促进小波的理论完善与应用研究具有十分重要的意义。     

Image representation using 2D Gabor wavelets

This paper extends to two dimensions the frame criterion developed by Daubechies for one-dimensional wavelets, and it computes the frame bounds for the particular case of 2D Gabor wavelets. Completeness criteria for 2D Gabor image representations are important because of their increasing role in many computer vision applications and also in modeling biological vision, since recent neurophysiological evidence from the visual cortex of mammalian brains suggests that the filter response profiles of the main class of linearly-responding cortical neurons (called simple cells) are best modeled as a family of self-similar 2D Gabor wavelets. We therefore derive the conditions under which a set of continuous 2D Gabor wavelets will provide a complete representation of any image, and we also find self-similar wavelet parametrization which allow stable reconstruction by summation as though the wavelets formed an orthonormal basis. Approximating a “tight frame” generates redundancy which allows low-resolution neural responses to represent high-resolution images     

基于特性分析的小波图像压缩性能研究

图象压缩时如何选择小波基是一个难题,这是由于不同的小波数学特性会对图象的压缩编码产生不同的影响.文中对小波基的正交性、光滑性、消失矩、滤波器长度等一些重要的小波特性对图象压缩性能的影响进行了对比研究.通过仿真分析,得出双正交小波比正交小波具有更优异的性能,一般条件下应尽量选择消失矩大、正则性好的双正交小波,而且应尽量优先保证重构小波的正则性效应,这样才可能得到效果较好的重构图像质量.但是在相同或相似的正则性、消失矩、滤波器长度等条件下,双正交小波较正交小波的性能改进则不是很明显.     

三种小波及其在图象压缩中的比较

介绍了小波家族中张量积小波、非张量积小波以及向量小波的发展及其特点，并根据小波的特点设计了测试图象，使其更好的体现小波的特征，对它们在测试图象中的分解特点进行了比较，从而对这三种小波有一个全面的认识。『     

Image forgery detection by semi-automatic wavelet soft-Thresholding with error level analysis

In this paper a method for detection of image forgery in lossy compressed digital images known as error level analysis (ELA) is presented and it’s noisy components are filtered with automatic wavelet soft-thresholding. With ELA, a lossy compressed image is recompressed at a known error rate and the absolute differences between these images, known as error levels, are computed. This method might be weakened if the image noise generated by the compression scheme is too intense, creating the necessity of noise filtering. Wavelet thresholding is a proven denoising technique which is capable of removing an image’s noise avoiding altering other components, like high frequencies regions, by thresholding the wavelet transform coefficients, thus not causing blurring. Despite its effectiveness, the choice of the threshold is a known issue. However there are some approaches to select it automatically. In this paper, a lowpass filter is implemented through wavelet thresholding, attenuating error level noises. An efficient method to automatically determine the threshold level is used, showing good results in threshold selection for the presented problems. This automatic threshold level can be fine tuned by a parameter k. Standard test images have been doctored to simulate image tampering, error levels for these images are computed and wavelet thresholding is performed to attenuate noise. Results are presented, confirming the method’s efficiency at noise filtering while preserving necessary error levels. The main contribution of this paper is the investigation of Daubechies wavelets with semi-automatic soft-thresholding in order to highlight forgeries in images. These results can be further extended by expert systems to classify and identify forgeries.     

Signal Representation by Adaptive Biased Wavelet Expansions

This paper reviews a technique of adaptive wavelet expansions and introduces the novel concept of “biased wavelets.” These are functions that are localized in time and in frequency but, unlike conventional wavelets, have an adjustable nonzero mean component. Under mild conditions, it is shown that a conventional mother wavelet can be used to construct a family of biased wavelets which spans the set of finite-energy functions L²( ). Numerical tests suggest that the introduction of the adjustable “bias” considerably improves the representation capabilities of wavelet expansions. A problem of electrocardiographic data compression is used for illustration purposes. Test signals were extracted from the MIT–BIH ECG Compression Test Database.     

方向性小波理论应用特性分析

方向性小波理论为图像处理提供了一种新的稀疏表示方法,能够更有效地捕捉图像中的几何结构。本文从基的特征入手,比较了方向性小波与传统小波在逼近图像几何边缘时的不同之处;总结了近年来该领域内提出的几种主要理论,以Ridgelet变换为例说明了方向性小波理论的基本原理。实验演示了Contourlet变换和小波变换的非线性逼近性能
能和去噪效果。最后指出了该领域进一步研究的方向     

基于主方向构造二分树复数小波的新方法

The conception of “main direction” of multi-dimensional wavelet is established in this paper, and the capabilities of several classical complex wavelets for representing directional singularities are investigated based on their main directions. It is proved to be impossible to represent directional singularities optimally by a multi-resolution analysis (MRA) of L2(R2). Based on the above results, a new algorithm to construct Q-shift dual tree complex wavelet is proposed. By optimizing the main direction of parameterized wavelet filters, the difficulty in choosing stop-band frequency is overcome and the performances of the designed wavelet are improved too. Furthermore, results of image enhancement by various multi-scale methods are given, which show that the new designed Q-shift complex wavelet do offer significant improvement over the conventionally used wavelets. Direction sensitivity is an important index to the performance of 2D wavelets.     

Texture classification using Gabor wavelets based rotation invariant features

Texture based image analysis techniques have been widely employed in the interpretation of earth cover images obtained using remote sensing techniques, seismic trace images, medical images and in query by content in large image data bases. The development in multi-resolution analysis such as wavelet transform leads to the development of adequate tools to characterize different scales of textures effectively. But, the wavelet transform lacks in its ability to decompose input image into multiple orientations and this limits their application to rotation invariant image analysis. This paper presents a new approach for rotation invariant texture classification using Gabor wavelets. Gabor wavelets are the mathematical model of visual cortical cells of mammalian brain and using this, an image can be decomposed into multiple scales and multiple orientations. The Gabor function has been recognized as a very useful tool in texture analysis, due to its optimal localization properties in both spatial and frequency domain and found widespread use in computer vision. Texture features are found by calculating the mean and variance of the Gabor filtered image. Rotation normalization is achieved by the circular shift of the feature elements, so that all images have the same dominant direction. The texture similarity measurement of the query image and the target image in the database is computed by minimum distance criterion.     

基于小波变换的数字耳蜗滤波器组设计与实现

分析了耳蜗滤波器与小波变换的相似性,以耳蜗频率响应为基础,设计出相应的小波变换基函数,并通过二进尺度变换得到一组小波作为耳蜗滤波器组。研究了利用该小波滤波器组进行多分辨率分析的数字实现方法,给出了相应的分析滤波器。理论和实验结果均表明,利用小波变换来实现耳蜗滤波器组是可行的。     

一种新型提升格式与改进的基于行编码图像压缩方法

本文首先提出了一种新型的提升格式,作为特例得到了含参数的具有简单有理系数的8-6小波。将基于行的图像编码方法进行改进并与新型提升格式相结合,提出了一种高保真、低存储、低复杂度的图像压缩方法,实验结果验证了方法的良好性能。     

JPEG2000中不同小波基的图像压缩性能分析

主要讨论了用JPEG2000标准进行静态图像压缩时，小波基的选择对图像压缩性能的影响．我们根据JPEG2000标准，比较了各类图像在不同小波基下的压缩结果，发现在JPEG2000中，小波基的选择在一定程度上影响了图像的压缩性能．对于某些图像，JPEG2000标准的缺省小波基并不能取得较优的压缩结果．文中分析了影响图像压缩性能的小波基与图像的特性，在此基础上，给出JPEG2000进行图像压缩时小波基的选择方法．     

Wavelet-based de-noising techniques in MRI

The paper deals with techniques for the enhancement of magnetic resonance (MR) images using the wavelet analysis, which is assessed from the viewpoint of choosing the mother wavelet and the thresholding technique. Three parameters are used as objective criteria of the quality of image enhancement: the signal-to-noise ratio (SNR), image contrast, and linear approximation of edge steepness. Unlike most of the standard methods, which work exclusively with image magnitude, we also examined the influence of image phase, i.e. the image is processed as a complex signal. In addition to the interpretation of results, a short summary is given that deals with the choice of the optimal mother wavelet and thresholding technique for different types of MR images.     

双正交小波滤波器组的提升构造与优化

从编码增益的角度,考察了双通道双正交小波图像编码系统的性能。首先,对双正交滤波器组的多相位矩阵进行提升分解,并结合消失矩和归一化条件,得到了含自由变量的提升参数。根据Vaidyanathan编码增益表达式求出编码增益的最优值。然后重点构造了三种9/7小波。尽管MIT小波的图像压缩质量略低于CDF 9/7小波,但它不仅系数简单,易于硬件实现,而且编码增益更大。这在编码器设计时具有重要实用价值。     

多小波变换的提升格式及其在图象编码中的应用

在简要介绍提升格式和多小波之后，提出了一种新的实现多小波变换的提升格式模型，由于这个模型主要由若干个单小波变换的提升格式搭建而成，因而不必自己推演提升格式的内部结构和参数，另外，这个模型还可以根据实际应用的需要选用不同的单小波，该文还给出用D9／7双正交（单）小波变换的提升格式构造的多小波变换的实例，并把这样构造的多小波变换应用于图象编码，结果表明，该方法可取得比常用的GHM多小波图象编码更好的效果。     

参数化的Deslauriers-Dubuc插值小波——构造及图像编码性能分析

研究了采用提升构造具有任意偶数阶消失矩, 满足对称性, 且仅用一个自由参数表达的 Deslauriers-Dubuc (D-D)双正交插值小波. 首先,采用多相矩阵理论推导出了此类小波存在的条件; 然后,给出了对应小波滤波器和插值小波变换的构造算法. 采用算法具体构造了分别具有消失矩对(4, 2)、(4, 4)、(6, 2)以及(6, 4) 等4类一参数表达的D-D插值小波; 最后, 以自由参数为自变量, 根据编码增益准则, 优化设计了4种用于图像编码的插值小波, 其滤波器系数全为二进制分数, 可实现非乘法运算的离散小波变换(Discrete wavelet transform, DWT). 系统分析表明, 两种小波的压缩性能超过CDF-9/7小波, 对于纹理图像, PSNR增益达到0.44.dB, 并且计算复杂度可降低17%以上. 实验同时表明, 新小波的重构图像具有更好的主观可视质量.     

基于小波零树图像编码算法的改进

小波变换具有良好空间-频率局部化特性,使小波变换后图像的能量大部分聚集到了低频子图像,利用原始图像在小波分解中不同分辨率级能量分布不均匀的特点,提出了改进的嵌入式小波零树编码算法-保持低频数据无损压缩编码的嵌入式小波零树编码。理论分析和实践表明,该方法能够降低重构图像的均方误差（MSE）、提高重构图像的峰值信噪比（PSNR）。     

基于二层自适应正交小波的疵点检测

本文提出了基于二层自适应正交小波的织物疵点检测方法。首先介绍了织物纹理图像的二维正交小波变换．在此基础上借鉴Daubechies小波构造过程，阐明了二层自适应正交小波的构造方法，然后对图象进行二层小波分解。分别比较无缺陷图像与待检测图像二层分解后的纬向和径向子图像，得到纬向和径向疵点信息，最后将两个方向上的疵点信息融合．得到检测结果。实验证明该方法是有效的。     

Comparison and improvement of wavelet‐based image fusion

The wavelets used in image fusion can be categorized into three general classes: orthogonal, biorthogonal, and non‐orthogonal. Although these wavelets share some common properties, each wavelet also has a unique image decomposition and reconstruction characteristic that leads to different fusion results. This paper focuses on the comparison of the image‐fusion methods that utilize the wavelet of the above three general classes, and theoretically analyses the factors that lead to different fusion results. Normally, when a wavelet transformation alone is used for image fusion, the fusion result is not good. However, if a wavelet transform and a traditional fusion method, such as an IHS transform or a PCA transform, are integrated, better fusion results may be achieved. Therefore, this paper also discusses methods to improve wavelet‐based fusion by integrating an IHS or a PCA transform. As the substitution in the IHS transform or the PCA transform is limited to only one component, the integration of the wavelet transform with the IHS or PCA to improve or modify the component, and the use of IHS or PCA transform to fuse the image, can make the fusion process simpler and faster. This integration can also better preserve colour information. IKONOS and QuickBird image data are used to evaluate the seven kinds of wavelet fusion methods (orthogonal wavelet fusion with decimation, orthogonal wavelet fusion without decimation, biorthogonal wavelet fusion with decimation, biorthogonal wavelet fusion without decimation, wavelet fusion based on the ‘à trous’, wavelet and IHS transformation integration, and wavelet and PCA transformation integration). The fusion results are compared graphically, visually, and statistically, and show that wavelet‐integrated methods can improve the fusion result, reduce the ringing or aliasing effects to some extent, and make the whole image smoother. Comparisons of the final results also show that the final result is affected by the type of wavelets (orthogonal, biorthogonal, and non‐orthogonal), decimation or undecimation, and wavelet‐decomposition levels.