PARAMETRIZATION OF BALANCED MULTIWAVELET

This paper deals with the parametrization of balanced multiwavelets and different properties associated with them. We introduce the property balancing symmetry and orthogonal properties of multiwavelet and link these properties to the matrix of the lowpass synthesis rnultifilter. Using these new results, we present the parametrization of orthogohal multiwavelets of flip-symmetry with length two and three. This is a direct construction method, making the construction of the balanced multiwavelet as easy as the scalar wavelet.

Digital watermarking algorithm based on neural network in multiwavelet domain

A novel blind digital watermarking algorithm based on neural networks and multiwavelet transform is presented. The host image is decomposed through multiwavelet transform. There are four subblocks in the LL- level of the multiwavelet domain and these subblocks have many similarities. Watermark bits are added to low- frequency coefficients. Because of the learning and adaptive capabilities of neural networks, the trained neural networks almost exactly recover the watermark from the watermarked image. Experimental results demonstrate that the new algorithm is robust against a variety of attacks, especially, the watermark extraction does not require the original image.

基于Multiwavelet广义高斯模型的图像盲隐写分析

针对目前图像盲隐写分析中提取的特征的有效性不高问题,提出了一种新的基于Multiwavelet广义高斯模型的图像盲隐写分析算法。采用Multiwavelet变换对样本图像进行多尺度分解,并使用广义高斯模型对每个子带的Multiwavelet系数进行建模,提取参数特征。利用这些参数特征训练支持向量机SVM(sup-port vector machine)构成盲隐写分析算法的分类检测器。通过对大量图像样本进行测试,实验结果表明,和经典的Farid方法相比,提出的盲隐写分析算法提取的图像特征更加有效,具有更高的正确检测率。

Sampling theorem for multiwavelet subspaces

Unlike scalar wavelets, multiscaling functions can be orthogonal, regular and symmetrical, and have compact support and high order of approximation simultaneously. For this reason, even if multiscaling functions are not cardinal, they still hold for perfect A/D and D/A. We generalize the Walter＇s sampling theorem to multiwavelet subspaces based on reproducing kernel Hilbert space. The reconstruction function can be expressed by multiwavelet function using the Zak transform. The general case of irregular sampling is also discussed and the irregular sampling theorem for multiwavelet subspaces established. Examples are presented.

PESEDOSPECTRAL-MULTIWAVELET-GALERKIN METHOD FOR ADVECTION-DIFFUSION PROBLEM WITH COMPLEX BOUNDARY

The element of pesedospectral-multiwavelet-Galerkin method, and how tocombine it with penalty method for treating boundary conditions are given. Multiwavelet bases don'toverlap on the given scale, and possess the same compact set in a group of several functions, sothey can be directly used to the numerical discretion on the finite interval. Numerical tests showthat general boundary conditions can be enforced with the penalty method, and thatpesedospectral-multiwavelet-Galerkin method can well track the solutions' development. This alsoproves that pesedospectral-multiwavelet-Galerkin method is effective.

High Efficiency Crypto-Watermarking System Based on Clifford-Multiwavelet for 3D Meshes Security

Since 3D mesh security has become intellectual property,3D watermarking algorithms have continued to appear to secure 3D meshes shared by remote users and saved in distant multimedia databases.The novelty of our approach is that it uses a new Clifford-multiwavelet transform to insert copyright data in a multiresolution domain,allowing us to greatly expand the size of the watermark.After that,our method does two rounds of insertion,each applying a different type of Clifford-wavelet transform.Before being placed into the Clifford-multiwavelet coefficients,the watermark,which is a mixture of the mesh description,source mesh signature(produced using SHA512),and a logo encrypted using the RSA(Ronald Shamir Adleman)technique,is encoded using Turbo-code.Using the Least Significant Bit method steps,data embedding involves modulation and insertion processes.Finally,the watermarked mesh is reconstructed using the inverse Cliffordmultiwavelet transform.Due to the utilization of a hybrid insertion domain,our technique has demonstrated a very high insertion rate while retaining mesh quality.The mesh is watermarked,and the extracted data is acquired in real-time.Our approach is also resistant to the most common types of attacks.Our findings reveal that the current approach improves on previous efforts.

Denoising of Medical Images Using Multiwavelet Transforms and Various Thresholding Techniques

The problem of estimating an image corrupted by additive white Gaussian noise has been of interest for practical reasons. Non-linear denoising methods based on wavelets, have become popular but Multiwavelets outperform wavelets in image denoising. Multiwavelets are wavelets with several scaling and wavelet functions, offer simultaneously Orthogonality, Symmetry, Short support and Vanishing moments, which is not possible with ordinary (scalar) wavelets. These properties make Multiwavelets promising for image processing applications, such as image denoising. The aim of this paper is to apply various non-linear thresholding techniques such as hard, soft, universal, modified universal, fixed and multivariate thresholding in Multiwavelet transform domain such as Discrete Multiwavelet Transform, Symmetric Asymmetric (SA4), Chui Lian (CL), and Bi-Hermite (Bih52S) for different Multiwavelets at different levels, to denoise an image and determine the best one out of it. The performance of denoising algorithms and various thresholding are measured using quantitative performance measures such as, Mean Square Error (MSE), and Root Mean Square Error (RMSE), Signal-to-Noise Ratio (SNR), Peak Signal-to-Noise Ratio (PSNR). It is found that CL Multiwavelet transform in combination with modified universal thresholding has given best results.

Construction of Biorthgonal Multiwavelets

Biorthogonal multiwavelets are generated from related scaling function vectors via multiresolution analysis. In this paper, we first show how to derive even-length biorthogonal lowpass filter pair from odd-length biorthogonal multiwavelet system with such properties as symmetry-antisymmetry and compactly support. So based on this, odd-length biorthogonal multiwavelet system can be constructed.

A CLASS OF MULTIWAVELETS AND PROJECTED FRAMES FROM TWO-DIRECTION WAVELETS

This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2（R^s）. Then, two theorems are given for constructing biorthogonal （orthogonal） two-direction refinable functions in L^2（R^s） and their biorthogonal （orthogonal） two-direction wavelets, respectively. From the constructed biorthogonal （orthogonal） two-direction wavelets, symmetric biorthogonal （orthogonal） multiwaveles in L^2（R^s） can be obtained easily. Applying the projection method to biorthogonal （orthogonal） two-direction wavelets in L^2（R^s）, we can get dual （tight） two-direction wavelet frames in L^2（R^m）, where m ≤ s. From the projected dual （tight） two-direction wavelet frames in L^2（R^m）, symmetric dual （tight） frames in L^2（R^m） can be obtained easily. In the end, an example is given to illustrate theoretical results.

Iris Identification Technology Based on Multiwavelets

A new method for iris identification based on multiwavelets is proposed. By means of the properties of multiwavelets, such as orthogonality, symmetry, vanishing moments and approximation order, the iris texture can be simply presented. A brief overview of muhiwavelets is presented at first. Iris identification system and iris texture feature presentation and recognition based on multiwavelets a,e introduced subsequently. And the experiment indicates the validity of this method finally.

Multiwavelets domain singular value features for image texture classification

A new approach based on multiwavelets transformation and singular value decomposition (SVD) is proposed for the classification of image textures. Lower singular values are truncated based on its energy distribution to classify the textures in the presence of additive white Gaussian noise (AWGN). The proposed approach extracts features such as energy, entropy, local homogeneity and max-min ratio from the selected singular values of multiwavelets transformation coefficients of image textures. The classification was carried out using probabilistic neural network (PNN). Performance of the proposed approach was compared with conventional wavelet domain gray level co-occurrence matrix (GLCM) based features, discrete multiwavelets transformation energy based approach, and HMM based approach. Experimental results showed the superiority of the proposed algorithms when compared with existing algorithms.

Simultaneous Speckle Reduction and SAR Image Compression Using Multiwavelet Transform

Synthetic aperture radar （SAR） images are corrupted by multiplicative speckle noise which limits the performance of the classical coder/decoder algorithm in spatial domain. The relatively new transform of multiwavelets can possess desirable features simultaneously, such as orthogonality and symmetry, while scalar wavelets cannot. In this paper we propose a compression scheme combining with speckle noise reduction within the multiwavelet framework. Compared with classical set partitioning in hierarchical trees （SPIHT） algorithm, our method achieves favorable peak signal to noise ratio （PSNR） and superior speckle noise reduction performances.

Application of AUSMPW scheme based on adaptive algorithm of multiwavelets in two dimensional flow field

In this paper,the AUSMPW scheme based on adaptive algorithm of multi-wavelets is presented to solve two dimensional Euler equations.This scheme based on the original AUSMPW scheme uses the multiwavelets for multi-level decomposition of the function and uses the method of the valve's value to construct adaptive grid to improve AUSMPW scheme.The obtained press and density have beed compared with those of results calculated by original AUSMPW scheme and WENO scheme.The numerical results demonstrate that this method has higher resolution.

Construction of Balanced Orthogonal Nonseparable Multiwavelets

A general method for constructing bidimensional orthogonal nonseparable mul- tiwavelets is presented. Moreover, this construction method can be extended to the con- struction of n-dimensional multiwavelets. In addition, we also study some properties of the multiwavelets such as balancing. Finally, we give an-example to illustrate our method to construct bidimensional nonseparable compactly supported orthogonal multiwavelets.

SMOOTHING OF 1/F SIGNAL WITH ORTHOGONAL MULTIWAVELET

Based on the orthogonal multiwavelet model of 1/f signals, smoothing fractal signals from white Gaussian noise with multiwavelet filter is proposed. The proposed multiwavelet method is very simple and easy to realize. Compared with Wornell's single wavelet method, the new method has r filtering factors at each scale and has higher filtering speed, where r is the multiplicity of multiwavelet. Also due to the advantages of multiwavelet, the multiwavelet method performs better than that of Wornell's. Simulation results verify the analysis, and Wornell's method is the special case of our method when r = 1.

Chebyshev Biorthogonal Multiwavelets and Approximation

In this paper, we construct Chebyshev biorthogonal multiwavelets, and use this multiwavelets to approximate signals (functions). The convergence rate for signal approximation is derived. The fast signal decomposition and reconstruction algorithms are presented. The numerical examples validate the theoretical analysis.

The Algorithm of Balanced Orthogonal Multiwavelets and Its Application in Denoising

In order to extract fault features of a weak signal from the strong noise and maintain signal smoothness, a new method of denoising based on the algorithm of balanced orthogonal multiwavelets is proposed. Multiwavelets have several scaling functions and wavelet functions, and possess excellent properties that a scalar wavelet cannot satisfy simultaneously, and match the different characteristics of signals. Moreover, the balanced orthogonal multiwavelets can avoid the Gibbs phenomena and their processes have the advantages in denoising. Therefore, the denoising based on the algorithm of balanced orthogonal multiwavelets is introduced into the signal process. The algorithm of bal- anced orthogonal multiwavelet and the implementation steps of this denoising are described. The experimental compar- ison of the denoising effect between this algorithm and the traditional multiwavelet algorithm was done. The experi- ments indieate that this method is effective and feasible to extract the fault feature submerged in heavy noise.

Face Identification Using Multiwavelet Transform and Multiwavelet Network

Interest in face identification systems has increased significantly due to the emergence of significant commercial opportunities in surveillance and security applications. In this paper, an approach is developed for combining the MWT （multiwavelet transform） with a MWN （multiwavelet network） as face identification algorithm. Only quarter of the approximation of the multiwavelet of the face image will be used as input to the MWN where the approximation quarter of the resultant multiwavelet of the face image will be segmented into four parts. These parts will be treated as 3D representation of the face image and will be given to the MWN. This makes multiwavelets a well designed tool for face identification. The multiwavelet shows promise in combining the desirable feature of the face image. A fast procedure for computing the MWT is introduced. The algorithm developed in this paper are tested on a data base consisting of 480 face images. The proposed algorithm outperform the other methods where a 100% identification was achieved using the mentioned data base.

Infrared Image Denoising Based on Single-wavelet and Multiwavelets

Deviation is essential to classic soft threshold denoising in wavelet domain. Texture features ofnoised image denoised by wavelet transform were weakened. Gibbs effect is distinct at edges of image.Image blurs comparing with original noised image. To solve the questions, a blind denoising method basedon single-wavelet transform and multiwavelets transform was proposed. The method doesn’t depend onsize of image and deviation to determine threshold of wavelet coefficients, which is different from classicalsoft-threshold denoising in wavelet domain. Moreover, the method is good for many types of noise. Gibbseffect disappeared with this method, edges of image are preserved well, and noise is smoothed andrestrained effectively.

融合多小波分解的深度卷积神经网络轴承故障诊断方法

针对卷积神经网络及其与信号降噪预处理集成方法面临高噪声环境和低质量数据挑战时难以有效地提取信号有用特征的问题,提出了一种融合Geronimo-Hardin-Massopust多小波分解的深度卷积神经网络模型(GHMMD-DCNN)。该模型思想是将多小波包分解与卷积神经网络深度融合,即设计多个一级多小波分解层以提取信号的低频分量和高频分量,再将多个一级多小波分解层与卷积层交替联接,使模型能够多尺度地提取并学习信号有用的时频域信息,信号分解和特征学习交替执行,进而实现强噪声鲁棒特征提取。在不同工况下的航空高速轴承振动数据上进行测试,结果表明:所提模型训练时能够快速达到稳定收敛,并且识别准确率均能达到99.9%以上;提出的方法在强噪声干扰下的故障辨识准确度和识别稳定性均优于对比方法,验证了其优秀的抗噪声干扰能力;在少训练样本测试中,提出的方法在单类训练样本数量为60时的平均诊断准确率高达91.19%,相比于其他方法最低提升了13.19%,验证了GHMMD-DCNN模型具有更优的低样本泛化能力。