非对称数字水印系统研究

针对传统对称水印的不足,设计并实现了一种用于版权保护的非对称图像水印系统。该系统采用三级认证结构:用户和认证机构分别拥有由私钥变换而成的不同的公钥,他们可以利用各自的公钥对数字产品进行两层检测,并且无法去除和伪造水印,只有掌握私钥的版权所有者才能进行最终的认证。实验表明:该水印的检测性能良好,同时对常规的图像处理方法具有较强的顽健性。与其它非对称水印相比,该水印系统不但抵御公开攻击的能力较强,而且可防止认证机构的欺骗行为,因而具有更高的安全性。     

JPEG2000及其编码系统的实现

随着多媒体技术应用领域的扩大，小波图像压缩研究日趋成熟。因此，国际标准化组织(ISO)指定了新一代的图像压缩标准：JPEG2000。首先介绍了JPEG2000的特点，然后介绍了JPEG2000的编码系统的实现过程，重点讨论了JPEG2000的技术核心：离散小波变换和EBCOT技术。最后，通过使用VC^ 6．0实现JPEG2000的编码算法，并对两种图像压缩格式进行了比较，给出了一个详细的实验结果。     

基于小波分形理论的股价指数信息量测度研究

本把小波分析和分形理论引入到股价指数时间序列的分析中，给出了股价指数波动复杂性的信息量测度方法——信息熵和分形维方法。通过对上证综指和深证成指1994年1月3日至2002年3月4日期间的数据进行的实证分析显示，两种方法均能刻画股价指数波动的复杂程度，这对初步了解我国股市场的波动规律有一定的实际意义。     

小波分析在图像消噪中的应用

针对图像消噪问题，提出了二维快速小波算法和改进小波包分析算法，通过对图像的消噪处理，二维快速小波算法消噪效果明显，但由于小波包分析算法对上一层的低频部分和高频部分同时进行细分，具有更为精确的局部分析能力，对小波包分析算法进行了改进，消除了频带混叠问题，其消噪效果更佳，可得到更为广泛的应用。     

SUPPRESSING THE COHERENT SPECKLE OF SAR IMAGES WITH WAVELET ANALYSIS

This paper studies Synthetic Aperture Radar (SAR) images contaminated by the coherent speckle noise with the multiresolution analysis of wavelet transform. This study shows that the influences of the speckle on different frequency components of the SAR image are different, and that the SAR image and the speckle have different manners of singularity. So, this paper presents a denoising method of wavelet analysis to reduce the speckle. Some experiments approve that this method not only suppresses the speckle effectively, but also preserves as much target characteristics of the original image as possible. It shows that this denoising method of wavelet analysis offers a very attractive alternative to suppress the coherent speckle noise of the SAR image.     

一种分数余弦变换及应用

定义了一种分数余弦变换的形式，用前两个整数阶余弦变换的线性叠加构造分数余弦变换。然后基于特征值及特征向量计算的方法将其扩展成K周期形式，推导了两种计算分数余弦变换的算法，并且讨论了与Pei定义的分数余弦变换之间的关系。最后探讨了其在音频信号数字水印中的应用。     

Combined analysis of the high sensitivity Fourier transform and ICLAS-VeCSEL absorption spectra of D2O between 8800 and 9520 cm

The absorption spectrum of dideuterated water, D₂O, has been recorded between 8800 and 9520 cm⁻¹ by intracavity laser absorption spectroscopy (ICLAS) based on a vertical external cavity system emitting laser (VeCSEL) and by high sensitivity Fourier Transform spectroscopy. The combined analysis of the spectra has allowed attributing 1223 transitions to the D₂O species. The spectrum assignment was performed on the basis of the recent results of variational calculations based on an optimized potential energy surface of D₂O. A set of 687 energy levels was derived from transitions assigned to eight upper vibrational states, 577 of them being reported for the first time. A detailed line list has been generated. The line intensities were retrieved mainly from the FTS spectrum and the absolute integrated intensities of the 2v₁ + v₂ + v₃ and the v₂ + 3v₃ bands dominating the spectrum have been determined.     

A matricial extension of the Helson-Sarason theorem and a characterization of some multivariate linearly completely regular processes

We generalize the theorems of Helson-Szegö and Helson-Sarason for matricial measures. We study two-weighted inequalities for the Hilbert transform in [0, 2π] and in R and give a characterization for the positivity of the angle between past and future of multivariate weakly stationary stochastic processes, in the discrete and the continuous case. We also characterize the multivariate weakly stationary stochastic processes that are linearly completely regular and study the rate of convergence of the maximal correlation coefficient.     

旋转场铁氧体变极化器

利用旋磁波导系统的耦合波方程，推出了旋转四磁极磁化场铁氧体波导的极化变换矩阵，分析了旋转场变极化器的基本原理及控制方式，给出了实验结果。     

Finite Integral Transform Solutions for Free Vibrations of Rectangular Thin Plates With Mixed Boundary Constraints北大核心CSCD

Analytical solutions, with unique research value, can serve as benchmarks for empirical formulas and numerical methods, a tool for rapid parameter analysis and optimization, and a theoretical basis for experimental designs. Conventional analytical methods, e.g., the Lévy solution method, are only applicable to mechanical problems of plates and shells with opposite simply-supported edges, which, however, may fail to obtain analytical solutions for the issues with complex boundary constraints. In recent years, the finite integral transform method for plate and shell problems was developed to deal with non-Lévy-type plates and shells, but it is still infeasible to solve the mixed boundary constrains-induced complex boundary value problems of higher-order partial differential equations. Herein, for the first time, the finite integral transform method was combined with the sub-domain decomposition technique to solve the free vibrations of rectangular thin plates with mixed boundary constraints. The rectangular plate was first divided into 2 sub-domains according to the mixed boundary constraints, and the 2 sub-domains were solved analytically with the finite integral transform method. Finally, the continuity conditions were introduced to obtain the analytical solution of the original problem. Based on the side spot-welded cantilever plates commonly used in engineering, the free vibration problem of a rectangular thin plate with 1 edge subjected to clamped-simply supported constraints and the other 3 edges free, was analyzed. The obtained natural frequencies and mode shapes are in good agreement with those from the finite element method as well as the solutions in literature, thus verifying the accuracy of the proposed method. The solution procedure of the finite integral transform method can be implemented based on the governing equations without any assumption of the solution form. Therefore, this strict analytical method is widely applicable to complex boundary value problems of higher-order partial differential equations for such mechanical problems of plates and shells. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.