Enhancing signal-to-noise ratio and resolution in low-field NMR relaxation measurements using post-acquisition digital filters

The traditional way to enhance signal-to-noise ratio (SNR) of nuclear magnetic resonance (NMR) signals is to increase the number of scans. However, this procedure increases the measuring time that can be prohibitive for some applications. Therefore, we have tested the use of several post-acquisition digital filters to enhance SNR up to one order of magnitude in time domain NMR (TD-NMR) relaxation measurements. The procedures were studied using continuous wave free precession (CWFP-T₁) signals, acquired with very low flip angles that contain six times more noise than the Carr–Purcell–Meiboom–Gill (CPMG) signal of the same sample and experimental time. Linear (LI) and logarithmic (LO) data compression, low-pass infinity impulse response (LP), Savitzky–Golay (SG), and wavelet transform (WA) post-acquisition filters enhanced the SNR of the CWFP-T₁ signals by at least six times. The best filters were LO, SG, and WA that have high enhancement in SNR without significant distortions in the ILT relaxation distribution data. Therefore, it was demonstrated that these post-acquisition digital filters could be a useful way to denoise CWFP-T₁, as well as CPMG noisy signals, and consequently reducing the experimental time. It was also demonstrated that filtered CWFP-T₁ method has the potential to be a rapid and nondestructive method to measure fat content in beef and certainly in other meat samples.     

Wavelet Collocation Methods for a First Kind Boundary Integral Equation in Acoustic Scattering

In this paper we consider a wavelet algorithm for the piecewise constant collocation method applied to the boundary element solution of a first kind integral equation arising in acoustic scattering. The conventional stiffness matrix is transformed into the corresponding matrix with respect to wavelet bases, and it is approximated by a compressed matrix. Finally, the stiffness matrix is multiplied by diagonal preconditioners such that the resulting matrix of the system of linear equations is well conditioned and sparse. Using this matrix, the boundary integral equation can be solved effectively.     

Entropy for frame bundle systems and Grassmann bundle systems induced by a diffeomorphism

A Liao hyperbolic diffeomorphism has equal measure entropy and topological entropy to that of its induced systems on frame bundles and Grassmann bundles. This solves a problem Liao posed in 1996 for Liao hyperbolic diffeomorphisms.     

Variational Derivative for Buckling Loads of Beams and Frames

The finite-difference method is a numerical technique for obtaining approximate solutions to differential equations. The main objective of the present study is to give a new aspect to the finite-difference method by using a variational derivative. By applying this formulation, accurate values of the buckling loads of beams and frames with various end supports are obtained. The performance of this formulation is verified by comparison with numerical examples in the literature __________ Published in Prikladnaya Mekhanika, Vol. 41, No. 7, pp. 139–144, July 2005.     

A Generalization of the Mean Size Formula of Wavelet Packets in Lp

The purpose of this paper is to investigate the mean size formula of wavelet packets in Lp for 0 〈 p ≤ ∞. We generalize a mean size formula of wavelet packets given in terms of the p-norm joint spectral radius and we also give some asymptotic formulas for the Lp-norm or quasi-norm on the subdivision trees. All results will be given in the general setting,     

一种小波域音频信息隐藏方法

提出了一种基于量化的小波域音频隐藏算法，将保密语音隐藏到载体音频中．为提高隐藏重和保密语音传输的安全性，对保密语音进行了小波域压缩编码和m序列的扩频调制，生成待隐藏的比特序列；通过量化方法，将编码和调制后的保密语音隐藏到载体音频的小波系数中；保密语音的恢复过程不需要使用原始音频、仿真结果表明，隐藏有保密语音的载体音频听觉质量没有明显下降，提取的保密语音感知质量较好；该算法对重量化、加噪、低通滤波等攻击均有良好的鲁棒性．     

Stable Ergodicity and Frame Flows

In this note we show that all diffeomorphisms close enough to the time-one map of the frame flow on certain negatively curved manifolds are ergodic. As a simple corollary we deduce that the frame flows are ergodic for all compact manifolds with curvature pinched sufficiently close to –1, thus providing results in the case of manifolds of dimension 7 or 8 which were missing from the results of Brin and Karcher.     

Geometry of an Accelerated Rotating Disk

We analyze the geometry of a rotating disk with a tangential acceleration in the framework of the theory of Special Relativity, using the kinematic linear differential system that verifies the relative position vector of time-like curves in a Fermi reference. A numerical integration of these equations for a generic initial value problem is made up and the results are compared with those obtained in other works.     

基于成像机理的小波包变换多聚焦图像融合

由于可见光成像系统的聚焦范围有限,因而在成像过程中,除聚焦良好的物体能生成清晰的图像外,该物体前后一定距离外的所有物体都将呈现不同程度的模糊.为了获得场景内所有物体均清晰的图像,在分析了多聚焦图像成像机理的基础上,提出了一种基于小波包变换的融合方法.它是将成像系统先聚焦在一部分对象上,得到其清晰的图像;然后再将其聚焦在另一部分对象上,得到另一清晰的图像;最后把这两幅实验图像加以融合,从而获得场景内所有物体均清晰的图像.实验结果表明,基于小波包变换的融合方法能够将信号的频带进行多层次划分,对高频成分也能进一步地分解,可有效综合多聚焦图像.     

利用小波变换进行海上目标识别研究

对海面舰船目标类型的识别,通常采用目视判读的方法。由于目视判读的方法不利于大面积侦察任务的快速识别,所以根据海上目标所具有的背景单一、结构复杂的特点,提出了利用小波变换所具有的多分辩率、易于消除噪声、运算方便的特点来提取舰船边缘特征,建立舰船结构特征数据库,实现舰船目标类型的自动判读。试验证明效果很好。