Construction of Multivariate Tight Framelet Packets Associated with Dilation Matrix

In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles.We also prove how to construct various tight frames for L2(Rd) by replac-ing some mother framelets.     

Optical asymmetric watermarking using modified wavelet fusion and diffractive imaging

In most of the existing image encryption algorithms the generated keys are in the form of a noise like distribution with a uniform distributed histogram. However, the noise like distribution is an apparent sign indicating the presence of the keys. If the keys are to be transferred through some communication channels, then this may lead to a security problem. This is because; the noise like features may easily catch people׳s attention and bring more attacks. To address this problem it is required to transfer the keys to some other meaningful images to disguise the attackers. The watermarking schemes are complementary to image encryption schemes. In most of the iterative encryption schemes, support constraints play an important role of the keys in order to decrypt the meaningful data. In this article, we have transferred the support constraints which are generated by axial translation of CCD camera using amplitude-, and phase- truncation approach, into different meaningful images. This has been done by developing modified fusion technique in wavelet transform domain. The second issue is, in case, the meaningful images are caught by the attacker then how to solve the copyright protection. To resolve this issue, watermark detection plays a crucial role. For this purpose, it is necessary to recover the original image using the retrieved watermarks/support constraints. To address this issue, four asymmetric keys have been generated corresponding to each watermarked image to retrieve the watermarks. For decryption, an iterative phase retrieval algorithm is applied to extract the plain-texts from corresponding retrieved watermarks.     

Signal enhancement of a novel multi-address coding lidar backscatters based on a combined technique of demodulation and wavelet de-noising

Multi-address coding (MAC) lidar is a novel lidar system recently developed by our laboratory. By applying a new combined technique of multi-address encoding, multiplexing and decoding, range resolution is effectively improved. In data processing, a signal enhancement method involving laser signal demodulation and wavelet de-noising in the downlink is proposed to improve the signal to noise ratio (SNR) of raw signal and the capability of remote application. In this paper, the working mechanism of MAC lidar is introduced and the implementation of encoding and decoding is also illustrated. We focus on the signal enhancement method and provide the mathematical model and analysis of an algorithm on the basis of the combined method of demodulation and wavelet de-noising. The experimental results and analysis demonstrate that the signal enhancement approach improves the SNR of raw data. Overall, compared with conventional lidar system, MAC lidar achieves a higher resolution and better de-noising performance in long-range detection.     

静态小波变换荧光检测水中矿物油信号的去噪方法

荧光分析法具有灵敏度高、选择性好、易于设计等优点,是检测水中油类污染物的重要手段。光电探测器产生的噪声会影响荧光检测系统的灵敏度,荧光信号的噪声消除一直是研究的热点问题。由于荧光信号增加了支集长度,dbN族小波能够解决信号的边界问题,通过比较dbN族不同小波基的去噪效果,选择db7为最优小波基,对含噪荧光信号作5层静态小波分解。根据小波熵理论自适应地选择阈值,高频系数经过阈值量化并重构得到纯净的荧光信号。与离散小波变换相比,静态小波变换去噪后信号具有信息完整性和时移不变性。     

花生种子品质的可见-近红外光谱分析

利用600~1 100 nm波段研究花生品种的可见-近红外反射光谱,对选取的三种具有代表性的花生种子进行实验。使用近红外光纤光谱仪采集光谱数据,对原始光谱进行小波分析以提取光谱特征,再用主成分分析方法进行聚类分析,最后把每一个样品的前4个主成分得分作为识别模型的输入,品种类别作为模型的输出,以马氏距离作为判别函数,建立了线性判别分析模型。对于每个品种的50个样品,随机挑选30个样本作为训练集,剩余的20个样本作为预测集。该识别模型对3个花生品种的平均正确识别率为95%。表明该方法能有效的识别花生种子,得到较好的分类效果,为花生种子品质的区分和鉴别提供了一种新方法。     

基于小波变换的便携式X射线荧光光谱仪检测模型的建立与改进

应用便携式X射线荧光光谱仪对土壤中Cr,Cu,Zn,As,Pb等重金属含量进行检测,每个样品扫描检测3次,利用小波阈值滤噪的方法对所测谱线进行光滑去噪处理后,根据土壤重金属的标准值和相应的计数率(取三次处理后检测谱线的平均值)建立各重金属的标准曲线。运用小波阈值滤噪方法时,为确定最佳的小波基和小波分解层数,以信噪比(SNR),均方根误差(MSE)和信息熵(H)作为评估指标评价降噪效果。为验证仪器的稳定性,根据土壤样品中重金属浓度的不同挑选部分样品并同时选用H3BO3(空白对照)进行重测。结果表明:运用小波变换方法时,选取coif3小波基对谱线进行三层分解,取得了最佳的去噪效果;建立好模型后,仪器的决定系数R2范围是0.990~0.996,表明在0~1 500mg·kg-1范围内,土壤样品中各重金属元素含量与X射线荧光光谱特征峰强度之间的线性关系良好;经过重复检测和计算得知仪器的检出限均低于国家一级土壤标准。将小波变换的方法实际运用到X射线荧光光谱仪检测模型的建立与改进中,有效的提高了模型的准确性,同时经验证,仪器具有良好的精密度,可运用于实际土壤重金属污染的现场快速筛查。     

Intertwining wavelets or multiresolution analysis on graphs through random forests

We propose a new method for performing multiscale analysis of functions defined on the vertices of a finite connected weighted graph. Our approach relies on a random spanning forest to downsample the set of vertices, and on approximate solutions of Markov intertwining relation to provide a subgraph structure and a filter bank leading to a wavelet basis of the set of functions. Our construction involves two parameters q and $q^{\prime }$. The first one controls the mean number of kept vertices in the downsampling, while the second one is a tuning parameter between space localization and frequency localization. We provide an explicit reconstruction formula, bounds on the reconstruction operator norm and on the error in the intertwining relation, and a Jackson-like inequality. These bounds lead to recommend a way to choose the parameters q and $q^{\prime }$. We illustrate the method by numerical experiments.     

Wavelet decomposition method decoupled boiling/evaporation oscillation mechanisms over two to three timescales: A study for a microchannel with pin fin structure

Boiling/evaporation heat transfer in a microchannel with pin fin structure was performed with water as the working fluid. Simultaneous measurements of various parameters were performed. The chip wall temperatures were measured by a high spatial-time resolution IR image system, having a sensitivity of 0.02 °C. The flow pattern variations synchronously changed wall temperatures due to ultra-small Bi number. The wavelet decomposition method successfully identified the noise signal and decoupled various temperature oscillations with different amplitudes and frequencies. Three types of temperature oscillations were identified according to heat flux q and mass flux G. The first type of oscillation occurred at q/G < 0.62 kJ/kg. The approximation coefficient of wavelet decomposition decided the dominant cycle period which was ∼3 times of the fluid residence time in the microchannel, behaving the density wave oscillation characteristic. The detail coefficients of wavelet decomposition decided the dominant cycle period, which matched the flow pattern transition determined value well, representing the flow pattern transition induced oscillation. For the second type of oscillation, the wavelet decomposition decoupled the three oscillation mechanisms. The pressure drop oscillation caused the temperature oscillation amplitudes of 5–10 °C and cycle periods of 10–15 s. The density wave oscillation and flow pattern transition induced oscillation are embedded with both the pressure rise and decrease stages of the pressure drop oscillation. The third type of oscillation happened at q/G > 1.13 kJ/kg, having the density wave oscillation coupled with the varied liquid film evaporation induced oscillation. The liquid island, retention bubble induced nucleation sites and cone-shape two-phase developing region are unique features of microchannel boiling with pin fin structure. This study illustrated that pressure drop oscillation and density wave oscillation, usually happened in large size channels, also take place in microchannels. The flow pattern transition and varied liquid film evaporation induced oscillations are specific to microchannel boiling/evaporation flow.     

Large deflection and post-buckling analysis of non-linearly elastic rods by wavelet method

We propose a wavelet method in the present study to analyze the large deflection bending and post-buckling problems of rods composed of non-linearly elastic materials, which are governed by a class of strong non-linear differential equations. This wavelet method is established based on a modified wavelet approximation of an interval bounded L²-function, which provides a new method for the large deflection bending and post-buckling problems of engineering structures. As an example, in this study, we considered the rod structures of non-linear materials that obey the Ludwick and the modified Ludwick constitutive laws. The numerical results for both large deflection bending and post-buckling problems are presented, illustrating the convergence and accuracy of the wavelet method. For the former, the wavelet solutions are more accurate than the finite element method and the shooting method embedded with the Euler method. For the latter, both bifurcation and limit loads can be easily and directly obtained by solving the extended systems. On the other hand, for the shooting method embedded with Runge–Kutta method, to obtain these values usually needs to choose a good starting value and repeat trial solutions many times, which can be a tough task.     

稀疏降噪自编码结合高斯过程的近红外光谱药品鉴别方法

提出一种稀疏降噪自编码结合高斯过程的近红外光谱药品鉴别方法。首先对近红外光谱数据进行小波变换以消除基线漂移,然后用稀疏降噪自编码(SDAE)网络提取光谱特征并降维表示,最后采用高斯过程(GP)进行二分类,其中GP选用光谱混合(SM)核函数作为协方差函数,记此分类网络为wSDAGSM。自编码网络具有很强的模型表示能力,高斯过程分类器在处理小样本数据时具有优势。wSDAGSM网络通过稀疏降噪自编码学习得到维数更低但更有价值的特征来表示输入数据,同时将具有很好表达力的光谱混合核作为高斯过程的协方差函数,有利于更准确的光谱数据分类。以琥乙红霉素及其他药品的近红外光谱为实验数据,将该方法与经过墨西哥帽小波变换的BP神经网络(wBP)、支持向量机(wSVM),SDAE结合Logistic二分类(wSDAL)、SDAE结合采用平方指数(SE)协方差核的GP二分类(wSDAGSE),以及未采用小波变换的SDAGSM网络等方法进行对比。实验结果表明,对光谱数据进行墨西哥帽小波变换预处理能有效提升SDAGSM网络的分类准确率和稳定性。wSDAGSM方法无论从分类准确率还是分类结果稳定性方面,都优于其他分类器。