Dyadic Bivariate Wavelet Multipliers in L^2（R@2）

The single 2 dilation wavelet multipliers in one-dimensional case and single A-dilation (where A is any expansive matrix with integer entries and |detA| = 2) wavelet multipliers in twodimensional case were completely characterized by Wutam Consortium (1998) and Li Z., et al. (2010). But there exist no results on multivariate wavelet multipliers corresponding to integer expansive dilation matrix with the absolute value of determinant not 2 in L ²(ℝ²). In this paper, we choose $2I_2 = \left( {{*{20}c} 2 & 0 \\ 0 & 2 \\ } \right)$2I_2 = \left( {\begin{array}{*{20}c} 2 & 0 \\ 0 & 2 \\ \end{array} } \right) as the dilation matrix and consider the 2I ₂-dilation multivariate wavelet Φ = {ψ ₁, ψ ₂, ψ ₃}(which is called a dyadic bivariate wavelet) multipliers. Here we call a measurable function family f = {f ₁, f ₂, f ₃} a dyadic bivariate wavelet multiplier if Y₁ = { F ^{- 1} ( f₁ [^(y₁ )] ),F ^{- 1} ( f₂ [^(y₂ )] ),F ^{- 1} ( f₃ [^(y₃ )] ) }\Psi _1 = \left\{ {\mathcal{F}^{ - 1} \left( {f_1 \widehat{\psi _1 }} \right),\mathcal{F}^{ - 1} \left( {f_2 \widehat{\psi _2 }} \right),\mathcal{F}^{ - 1} \left( {f_3 \widehat{\psi _3 }} \right)} \right\} is a dyadic bivariate wavelet for any dyadic bivariate wavelet Φ = {ψ ₁, ψ ₂, ψ ₃}, where [^(f)]\hat f and F ⁻¹ denote the Fourier transform and the inverse transform of function f respectively. We study dyadic bivariate wavelet multipliers, and give some conditions for dyadic bivariate wavelet multipliers. We also give concrete forms of linear phases of dyadic MRA bivariate wavelets.     

关于Parseval框架小波的刻画

In this paper,we characterize all generalized low pass filters and MRA Parseval frame wavelets in L 2 （R n ） with matrix dilations of the form （Df）（x） =√ 2f（Ax）,where A is an arbitrary expanding n × n matrix with integer coefficients,such that ｜det A｜ = 2.We study the pseudo-scaling functions,generalized low pass filters and MRA Parseval frame wavelets and give some important characterizations about them.Furthermore,we give a characterization of the semiorthogonal MRA Parseval frame wavelets and provide several examples to verify our results.     

Tight wavelet frames for irregular multiresolution analysis

An important tool for the construction of tight wavelet frames is the Unitary Extension Principle first formulated in the Fourier-domain by Ron and Shen. We show that the time-domain analogue of this principle provides a unified approach to the construction of tight frames based on many variations of multiresolution analyses, e.g., regular refinements of bounded L-shaped domains, refinements of subdivision surfaces around irregular vertices, and nonstationary subdivision. We consider the case of nonnegative refinement coefficients and develop a fully local construction method for tight frames. Especially, in the shift-invariant setting, our construction produces the same tight frame generators as the Unitary Extension Principle.     

A technique for flow-enhanced magnetic resonance angiography of the lower extremities

A two-dimensional, flow-enhanced gradient echo pulse sequence for nuclear magnetic resonance angiography is described. It employs interleaved, presaturated slices to acquire data efficiently on imagers which favor interleaved acquisition over sequential acquisition for multislice imaging. It is useful on any imager when the effective TR is extended to enhance the sensitivity to slow flow. The technique was applied to the region from aortic bifurcation to the iliac bifurcations of three normal volunteers. The right and left common iliac arteries and veins, the separation of the external and internal iliac arteries, and secondary branches were clearly depicted.     

基于EEMD-MRA方法的LIBS信号处理研究

LIBS技术优点众多,但由于光谱噪声干扰和基体效应等因素,影响了分析的准确度[1];EEMD方法能清晰的将LIBS信号中的不同特征成分自适应的分解开来。MRA方法能够补偿元素信号之间的互干扰,可进一步提高LIBS信号的准确性。通过自行搭建的测试系统获得了标准样品的原始信号,使用EEMD-MRA方法进行处理后,元素浓度曲线的决定系数R2得到了极大的提高,大大的提高数据的准确性,为LIBS信号的处理提供了一种全新的方式。     

E-紧框架小波来自MRA的特征刻画

设E=■或■,■(x)∈L~2(R~2)且■_(jk)(x)=2■(E~jx-k),其中j∈Z,k∈Z~2.若{■_(jk)|jJ∈Z,k∈Z~2}构成L~2(R~2)的紧框架,则称■(x)为E-紧框架小波.本文给出E-紧框架小波是MRA E-紧框架小波的一个充要条件,即E紧框架小波■来自多尺度分析当且仅当线性空间F_■(ξ)的维数为0或1,其中F_■(ξ)=■(ξ)|j■1},■_j(ξ)={■((E~T)~j(ξ+2kπ))}_(k∈EZ~2,j■1。     

Y. Meyer小波的一般形式

首先我们证明了，如果尺度函数有紧支集，来自多尺度分析的小波函数的支集形式，然后我们证明了Y．Meyer小波的尺度函的一般形式。最后给出了它的另外两种形式和对应的Y．Meyer小波。     

Whole-body MR angiography using variable density sampling and dual-injection bolus-chase acquisition

Conventional bolus-chase acquisition generates peripheral runoff images using a single injection of the contrast material. Low spatial resolution, small slice coverage and venous contamination are major problems especially in the distal stations. A technique is presented herein in which whole-body magnetic resonance angiography is performed using a dual-contrast-injection four-station acquisition protocol. Bolus sharing was performed between two stations: the abdomen and calf stations share the first bolus injection, while the thorax and thigh stations share the second bolus injection. The combination of variable density sampling and elliptical centric acquisition order was applied to the abdomen and thorax stations. The scan time was extended to generate high spatial resolution arterial phase images with broad slice coverage for the calf and thigh stations. The feasibility of this technique was demonstrated using phantom and in vivo human volunteer studies.     

Reduction of flow- and eddy-currents-induced image artifacts in coronary magnetic resonance angiography using a linear centric-encoding SSFP sequence

Coronary magnetic resonance angiography (MRA) acquired using steady-state free precession (SSFP) sequences tends to suffer from image artifacts caused by local magnetic field inhomogeneities. Flow- and gradient-switching-induced eddy currents are important sources of such phase errors, especially under off-resonant conditions. In this study, we propose to reduce these image artifacts by using a linear centric-encoding (LCE) scheme in the phase-encoding (PE) direction. Abrupt change in gradients, including magnitude and polarity between consecutive radiofrequency cycles, is minimized using the LCE scheme. Results from numeric simulations and phantom studies demonstrated that signal oscillation can be markedly reduced using LCE as compared to conventional alternating centric-encoding (ACE) scheme. The image quality of coronary arteries was improved at both 1.5 and 3.0 T using LCE compared to those acquired using ACE PE scheme (1.5 T: ACE/LCE=2.2+/-0.8/3.0+/-0.6, P=.02; 3.0 T: ACE/LCE=2.1+/-1.1/3.0+/-0.8, P=.01). In conclusion, flow- and eddy-currents-induced imaging artifacts in coronary MRA using SSFP sequence can be markedly reduced with LCE acquisition of PE lines.