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.

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.

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.

Construction of multiwavelets with high approximation order and symmetry

In this paper, based on existing symmetric multiwavelets, we give an explicit algorithm for constructing multiwavelets with high approximation order and symmetry. Concretely, suppose Φ(x) := (φ1(x), . . . , φr(x))T is a symmetric refinable function vectors with approximation order m. For an arbitrary nonnegative integer n, a new symmetric refinable function vector Φnew(x) := (φn1 ew(x), . . . , φrn ew(x))T with approximation order m + n can be constructed through the algorithm mentioned above. Additionally, we reveal the relation between Φ(x) and Φnew(x). To embody our results, we construct a symmetric refinable function vector with approximation order 6 from Hermite cubics which provides approximation order 4.

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。

A Wavelet-Free Approach for Multiresolution-Based Grid Adaptation for Conservation Laws

In recent years the concept of multiresolution-based adaptive discontinuous Galerkin(DG)schemes for hyperbolic conservation laws has been developed.The key idea is to perform a multiresolution analysis of the DG solution using multiwavelets defined on a hierarchy of nested grids.Typically this concept is applied to dyadic grid hierarchies where the explicit construction of the multiwavelets has to be performed only for one reference element.For non-uniform grid hierarchies multiwavelets have to be constructed for each element and,thus,becomes extremely expensive.To overcome this problem a multiresolution analysis is developed that avoids the explicit construction of multiwavelets.

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.

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.

Linear scaling Coulomb interaction in the multiwavelet basis,a parallel implementation

We present a parallel and linear scaling implementation of the calculation of the electrostatic potential arising from an arbitrary charge distribution.Our approach is making use of the multi-resolution basis of multiwavelets.The potential is obtained as the direct solution of the Poisson equation in its Green’s function integral form.In the multiwavelet basis,the formally non local integral operator decays rapidly to negligible values away from the main diagonal,yielding an effectively banded structure where the bandwidth is only dictated by the requested accuracy.This sparse operator structure has been exploited to achieve linear scaling and parallel algorithms.Parallelization has been achieved both through the shared memory(OpenMP)and the message passing interface(MPI)paradigm.Our implementation has been tested by computing the electrostatic potential of the electronic density of long-chain alkanes and diamond fragments showing(sub)linear scaling with the system size and efficent parallelization.

Gearbox fault diagnosis of rolling mills using multiwavelet sliding window neighboring coefficient denoising and optimal blind deconvolution

Fault diagnosis of rolling mills, especially the main drive gearbox, is of great importance to the high quality products and long-term safe operation. However, the useful fault information is usually submerged in heavy background noise under the severe condition. Thereby, a novel method based on multiwavelet sliding window neighboring coefficient denoising and optimal blind deconvolution is proposed for gearbox fault diagnosis in rolling mills. The emerging multiwavelets can seize the important signal processing properties simultaneously. Owing to the multiple scaling and wavelet basis functions, they have the supreme possibility of matching various features. Due to the periodicity of gearbox signals, sliding window is recommended to conduct local threshold denoising, so as to avoid the "overkill" of conventional universal thresholding techniques. Meanwhile, neighboring coefficient denoising, considering the correlation of the coefficients, is introduced to effectively process the noisy signals in every sliding window. Thus, multiwavelet sliding window neighboring coefficient denoising not only can perform excellent fault extraction, but also accords with the essence of gearbox fault features. On the other hand, optimal blind deconvolution is carried out to highlight the denoised features for operators' easy identification. The filter length is vital for the effective and meaningful results. Hence, the foremost filter length selection based on the kurtosis is discussed in order to full benefits of this technique. The new method is applied to two gearbox fault diagnostic cases of hot strip finishing mills, compared with multiwavelet and scalar wavelet methods with/without optimal blind deconvolution. The results show that it could enhance the ability of fault detection for the main drive gearboxes.

Riesz multiwavelet bases generated by vector refinement equation

In this paper, we investigate compactly supported Riesz multiwavelet sequences and Riesz multiwavelet bases for L2(Rs). Suppose ψ = (ψ1, . . . , ψr)T and ψ = ( ψ1, . . . , ψr)T are two compactly supported vectors of functions in the Sobolev space (Hμ(Rs))r for some μ > 0. We provide a characterization for the sequences {ψjk : = 1, . . . , r, j ∈ Z, k ∈ Zs} and {ψ jk : = 1, . . . , r, j ∈ Z, k ∈ Zs} to form two Riesz sequences for L2(Rs), where ψjk = mj/2ψ (M j ·k) and ψjk = mj/2 ψ (M j ·k), M is an s × s integer matrix such that limn→∞ Mn = 0 and m = |detM|. Furthermore, let = (1, . . . , r)T and = ( 1, . . . , r)T be a pair of compactly supported biorthogonal refinable vectors of functions associated with the refinement masks a, a and M, where a and a are finitely supported sequences of r × r matrices. We obtain a general principle for characterizing vectors of functions ψν = (ψν1, . . . , ψνr)T and ψν = ( ψν1, . . . , ψ?νr)T , ν = 1, . . . , m 1 such that two sequences {ψjνk : ν = 1, . . . , m 1, = 1, . . . , r, j ∈ Z, k ∈ Zs} and {ψ jνk : ν = 1, . . . , m 1, = 1, . . . , r, j ∈ Z, k ∈ Zs} form two Riesz multiwavelet bases for L2(Rs). The bracket product [f, g] of two vectors of functions f, g in (L2(Rs))r is an indispensable tool for our characterization.

Sampling theorem for multiwavelet subspaces

Sampling theorem on multiwavelet subspaces is established. Necessary and sufficient conditions are obtained. The result covers the Shannon’s sampling theorem and the early results on the sampling theorem for wavelet subspaces.

Multiwavelet sampling theorem in Sobolev spaces

This paper is to establish the multiwavelet sampling theorem in Sobolev spaces. Sampling theorem plays a very important role in digital signal communication. The most classical sampling theorem is Shannon sampling theorem, which works for bandlimited signals. Recently, sampling theorems in wavelets or multiwavelets subspaces are extensively studied in the literature. In this paper, we firstly propose the concept of dual multiwavelet frames in dual Sobolev spaces (H s (R) , H-s (R)). Then we construct a special class of dual multiwavelet frames, from which the multiwavelet sampling theorem in Sobolev spaces is obtained. That is, for any f ∈ H s (R) with s > 1/2, it can be exactly recovered by its samples. Especially, the sampling theorem works for continuous signals in L 2 (R), whose Sobolev exponents are greater than 1 /2.