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.     

Invariant discrete flows

In this paper, we investigate the evolution of joint invariants under invariant geometric flows using the theory of equivariant moving frames and the induced invariant discrete variational complex. For certain arc length preserving planar curve flows invariant under the special Euclidean group , the special linear group , and the semidirect group , we find that the induced evolution of the discrete curvature satisfies the differential‐difference mKdV, KdV, and Burgers' equations, respectively. These three equations are completely integrable, and we show that a recursion operator can be constructed by precomposing the characteristic operator of the curvature by a certain invariant difference operator. Finally, we derive the constraint for the integrability of the discrete curvature evolution to lift to the evolution of the discrete curve itself.     

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.     

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．     

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。     

一类常微分方程组的紧支撑样条小波方法探讨

应用三次紧支撑样条小波插值函数得到了求一类常微分方程组数值解的隐式公式,并求得到其局部截断误差为O(-h5).在此基础上给出1个显式校正求解公式,并讨论得到其局部截断误差为O(-h4).     

Locally Adaptive Wavelet Empirical Bayes Estimation of a Location Parameter

The traditional empirical Bayes (EB) model is considered with the parameter being a location parameter, in the situation when the Bayes estimator has a finite degree of smoothness and, possibly, jump discontinuities at several points. A nonlinear wavelet EB estimator based on wavelets with bounded supports is constructed, and it is shown that a finite number of jump discontinuities in the Bayes estimator do not affect the rate of convergence of the prior risk of the EB estimator to zero. It is also demonstrated that the estimator adjusts to the degree of smoothness of the Bayes estimator, locally, so that outside the neighborhoods of the points of discontinuities, the posterior risk has a high rate of convergence to zero. Hence, the technique suggested in the paper provides estimators which are significantly superior in several respects to those constructed earlier.     

A TVD Type Wavelet-Galerkin Method for Hamilton-Jacobi Equations

In this paper,we use Daubechies scaling functions as test functions for the Galerkin method,and discuss Wavelet-Galerkin solutions for the Hamilton-Jacobi equations.It can be proved that the schemesare TVD schemes.Numerical tests indicate that the schemes are suitable for the Hamilton-Jacobi equations.Furthermore,they have high-order accuracy in smooth regions and good resolution of singularities.