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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## CS代写|图像处理作业代写Image Processing代考|Impulse (Salt and Pepper) Noise

The PDF of random variables corresponding to impulse noise can be represented as:
$$p(z)=\left{\begin{array}{lll} P_a & \text { if } & z=a \ P_b & \text { if } & z=b \ 0 & \text { otherwise } & \end{array}\right.$$
where $P_a$ and $P_b$ are the noise densities. An example of the probability density function of impulse noise is shown in Figure 2.3. Its distribution is equivalent to two delta pulses at $z=a$ and $z=b$.

In general, the noise pulse can be positive or negative. Because the impact of pulse is often greater than the intensity of the signal in the image, impulse noise is generally quantified into the ultimate gray scale in the image (displayed as white or black). In practice, it is generally assumed that both $a$ and $b$ are “saturated” values, that is, they take the maximum and minimum gray levels allowed by the image. If $b>a$, the pixel with gray level $b$ is displayed as a white point in the image, and the pixel with gray level $a$ is displayed as a black point in the image. If $P_a$ or $P_b$ is 0 , impulse noise is called unipolar noise. If both $P_a$ and $P_b$ are not 0 , especially when the two values are very close, impulse noise is like salt and pepper grains randomly scattered on the image. For this reason, bipolar impulse noise is also called salt and pepper noise. In the image display, negative pulses are displayed as black (pepper noise) and positive pulses are displayed as white (salt noise). For 8-bit images, there are $a=0$ (black) and $b=255$ (white). Error exchange, shot noise, and spike noise can all be described by the probability density function of impulse noise.

The PDF of the random variable corresponding to uniform noise can be represented as $(a$ and $b$ are the upper and lower limits of the random variable value):
The mean and variance of uniform noise are respectively:
\begin{aligned} \mu &=(a+b) / 2 \ \sigma^2 &=(b-a)^2 / 12 \end{aligned}
An example of the probability density function of uniform noise is shown in Figure 2.4. The gray value of uniform noise is evenly distributed within the defined range, that is, statistically, the probability of all values appearing is equal.

Uniform noise density is often used as the basis of many random number generators. For example, it can be used to generate Gaussian noise.

## CS代写|图像处理作业代写Image Processing代考|IMAGE FILTERING AND DE-NOISING

Image filtering and de-noising refers to the use of image enhancement techniques to eliminate noise (Zhang 2017). Image enhancement technology is the most basic and most commonly used image processing technology, and it is also often used as a pre-processing technique before using other image technologies. The purpose of image enhancement is to transform the processed image into an image with “better” visual quality and more “useful” for the particular application through specific processing of the image. Because the $^{\prime \prime}$ purpose and requirements of each specific application are different, the meanings of “better” and “useful” here are not the same. Fundamentally, there is no universal standard for image enhancement. For each image processing application, the observer is the ultimate judge of the pros and cons of the enhancement technology. Since visual inspection and evaluation are quite subjective processes, the definition of a so-called “good image” is not fixed and often varies from person to person.

When using image enhancement technology to eliminate noise, it does not pay special attention to the cause of noise, but according to people’s general understanding of image quality, various methods are applied to enhance visual effects for image processing to reduce the impact of noise on image visual quality.Noise elimination based on image enhancement mainly adopts filtering modes, which can be performed in the spatial domain or in the frequency domain; it can also be performed automatically or interactively.

# 图像处理代考

## CS代写|图像处理作业代写Image Processing代考|Impulse (Salt and Pepper) Noise

\begin{aligned} &\ \ \ &p(z)=\backslash \text { left }{ \end{aligned}
$P_a \quad$ if $\quad z=a P_b \quad$ if $\quad z=b 0 \quad$ otherwise

$\$ \$$在哪里 P_a 和 P_b 是噪声密度。脉冲噪声的概率密度函数示例如图 2.3 所示。它的分布相当于两个增量脉冲在 z=a 和 z=b. 一般来说，噪声脉冲可以是正的或负的。由于脉冲的影响往往大于图像中信号的强度，因此脉冲噪声一般量化为图像中的最终灰度（显示为白色或黑 色) 。在实践中，通常假设两者 a 和 b 是”饱和”值，即它们取图像允许的最大和最小灰度级。如果 b>a, 具有灰度的像素 b 在图像中显示为一个白点， 并且该像素具有灰度 a 在图像中显示为一个黑点。如果 P_a 或者 P_b 为 0 时，脉冲噪声称为单极噪声。如果两者 P_a 和 P_b 不为 0 ，尤其是当两个值非常接 近时，脉冲橾声就像盐粒和胡标粒一样随机散布在图像上。因此，双极脉冲噪声也称为椒盐噪声。在图像显示中，负脉冲显示为黑色（胡椒噪声)， 正脉冲显示为白色 (盐噪声) 。对于 8 位图像，有 a=0 (黑色) 和 b=255 (白色的)。误差交换、散粒噪声和尖峰噪声都可以用脉冲噪声的概率 密度函数来描述。 均匀㖏声对应的随机变量的 PDF 可以表示为 (a 和 b 是随机变量值的上下限 ) ： 均匀噪声的均值和方差分别为:$$
\mu=(a+b) / 2 \sigma^2 \quad=(b-a)^2 / 12


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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

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