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The Laplace Transform; The Region of Convergence for Laplace Transforms; The Inverse Laplace Transform; Geometric Evaluation of the Fourier Transform from the Pole-Zero Plot; Properties of the Laplace Transform; Analysis and Characterization of LTI Systems Using the Laplace Transform; System Function

教学内容：拉普拉斯变换；拉普拉斯变换收敛域；拉普拉斯反变换；由零极点图对傅立叶变换进行几何求值；拉普拉斯变换性质；常用拉普拉斯变换对；用拉普拉斯变换分析和表征线性时不变系统；系统函数的代数属性与方框图表示；单边拉普拉斯变换。

We establish the relation of inversion formulas among generalized Radon transform with known weight functions, the exponential Radon transform and classical Radon transform, furthermore obtain approximate inversion formula of the exponential Radon transform, the idea of approach above is applied to contour reconstruction and is generalized to n-dimentional euclidean space case. We discuss the support theorem, range condition of the exponential Radon transform.

本文建立了带权广义Radon变换、指数型Radon变换与古典Radon变换反演公式的关系，从而得到指数型Radon变换的近似反演公式，并且应用这种思想方法于轮廓重构，并将这一结果推广到任意维欧氏空间的情形；讨论了指数型Radon变换的支集定理及值域条件。

For fast orthogonal transformation algorithm, the paper carries out detailed research and analysis. In terms of many transform coding, it put forward these four rapid transformation algorithms which are Discrete Cosine Transform, Discrete Fourier Transform, Harr Transform, Walsh-Handmaid Transform, and analysis of these fast algorithms in image compression applications.

对于正交变换的快速算法本文进行了详细的研究与分析，并根据各种变换编码，提出了离散余弦变换、离散傅立叶变换、Harr变换、Walsh-Hadamard变换这四种变换的快速算法，并分析了这些快速算法在图象压缩中的应用。

This paper introduces eight methods of tlme-frequency analysis, such as Hilbert transform, Hilbert-Huang transform, sine curve fitting, Ricker wavelet matching, short time Fourier transform, wavelet transform, S transform and Cohen methods, This paper explains the merits and defects of those methods from the time resolution, frequency resolution and the adaptive ability of multi-frequency signals.

本文介绍了Hilbert变换、Hilbert—Huang变换、正弦曲线拟合、雷克子波匹配、短时傅立叶变换、小波变换、S变换以及Cohen娄这八种方法，并从时间分辨率、频率分辨率，以及对多频率成份信号适应能力等各方面阐述了各种方法的优缺点，对其中的一些方法结合了理论记录进行了试算，进一步阐述了这些方法的长处和不足之处。

To increase the security of the watermark, a new binary image encryption algorithm based on TD-ERCS map is presented. The watermark is encrypted by a chaos sequence generated by TD-ERCS map; A novel color image watermarking algorithm is proposed based on discrete chaotic map and 2-dimensions discrete wavelet transform. The watermark is encrypted by the new binary image encryption algorithm, and the encrypted watermark is embed into four sub-bands of the most deep level of blue branch of host image by three-level wavelet transform, and the embedded positions are determined by general cat cha otic map; A novel color-image blind detection watermarking algorithm is proposed based on integer wavelet transform and subsampling. The scrambled watermark is encrypted and embed into the low sub-bands after four sub-images of the Y branch of host image is transformed by two-level wavelet transform, and the embedded positions are determined by Logistic chaotic map, this watermarking scheme can realize blind extraction.

为了提高水印图像的安全性，提出了一种基于TD-ERCS混沌映射的二值水印图像的加密算法，该算法利用TD-ERCS映射产生的混沌序列加密水印图像；将离散混沌映射和二维离散小波变换相结合，研究了彩色图像水印新算法，该算法先对混沌序列加密后的水印图像进行小波变换，再嵌入到宿主图像的蓝色分量的最深层的四个子带中，嵌入位置则由广义猫映射确定；将整数小波变换和图像子采样技术应用于数字水印，提出了一种彩色图像盲提取水印算法，水印嵌入时，先对宿主图像在YIQ色彩空间中的Y分量进行子采样，并对得到的四个子图像分别进行二级离散小波变换，然后将置乱并加密后的水印图像嵌入到小波变换后的低频子带中，其嵌入位置由Logistic混沌映射产生的混沌序列确定，实现了水印的盲提取。

At present, most of the image watermarking algorithms based on the wavelet transform fail to take into account the shortcoming that the first generation wavelet transform used in image processing will introduce quantization errors inevitably, because of the storing characteristics of the image. Wavelet transform that maps integers to integers will not introduce quantization errors. Its time-frequency analysis method and multi-scale property accordant with human being vision system makes integer wavelet transform an ideal way for digital watermarking.

目前，大多数基于小波变换的图像水印算法没有考虑到第一代小波变换用于图像处理中不可避免的引入量化误差的缺点，而整数小波变换除了具有小波的多分辨率分析与人类视觉特性一致、具有良好的时频特性等优点以外，还避免了第一代小波变换用于图像处理中引入量化误差等缺点。

SIFT（Scale Invariant Feature Transform） local feature is chosen because of its scale invariance and the property of accurate key-point localization.The Euclidean distance between different SIFT feature vectors is defined as the measure of similarity to get the pre-matched key-point pairs.The affine transform model is used to realize the registration.In order to get the accurate affine transform parameter,the principal of affine transform error is used to get rid of mismatched key-point pairs from the pre-matched pairs.

该方法选取具有良好尺度、旋转不变性以及精确特征点定位能力的SIFT局部特征，使用其特征向量间的欧氏距离作为相似性度量进行特征点匹配，并依据仿射变换误差准则去除奇异匹配特征点对，采用仿射变换的几何模型，实现了遥感图像的快速自动配准。

In order to overcome the aliasing phenomenon commonly existing in real contourlet transform image denoising, some characters of complex contourlet transform whose structure is a cascading of dual tree complex wavelet and directional filter banks are discussed. It is proved that the transform performs well at division and restraining ability under white Gaussian noise condition. Then, an image denoising algorithm was proposed based on the transform.

为了克服实轮廓波图像消噪后广泛存在的混叠现象，研究了基于双树复小波级联方向滤波器架构的复轮廓波变换图像消噪的若干性质，证明了对于高斯白噪声图像，该变换具有更好的分割能力和抑制能力，并在此基础上提出了一种基于该变换的图像消噪算法。

This paper mainly discussed the design of the image transform technology, which includes the analyse of the algorithms about fourier transform, discrete cosine transform and radon transform, proposed new improved algorithms, detailed di...

本文重点论述了图像变换技术部分的设计，对其中的傅立叶变换、离散余弦变换和Radon变换算法都做了详细的分析，提出了改进的算法，并详细论述了图像变换模块的设计过程，最后通过实例对各算法进行了具体说明。

Mastery: The Z-Transform, The Region of Convergence for the Z-Transform, The Inverse Z-Transform, Properties of the Z-Transform, System Function Algebra and Block Diagram Representations.

教学内容： Z 变换； Z 变换收敛域；逆 Z 变换；由零极点图对傅立叶变换进行几何求值； Z 变换性质；几个常用 Z 变换对；利用 Z 变换分析和表征线性时不变系统；系统函数的代数属性与方框图表示；单边 Z 变换。

But this is impossible, as long as it is engaging in a market economy, there are risks in any operation.

但是，这是不可能的，只要是搞市场经济，是有风险的任何行动。

We're on the same wavelength.

我们是同道中人。