EM (Expectation Maximization)算法是统计学中的核心算法,也是本校近代数理统计课程教学过程中的一个重难点。论文采用案例式、启发式、研讨式教学方法,以基于高斯混合模型(GMM)的轴承退化阶段划分问题为例,引导学生发现隐变量模型极...EM (Expectation Maximization)算法是统计学中的核心算法,也是本校近代数理统计课程教学过程中的一个重难点。论文采用案例式、启发式、研讨式教学方法,以基于高斯混合模型(GMM)的轴承退化阶段划分问题为例,引导学生发现隐变量模型极大似然估计(MLE)存在的困难,设计问题链启发学生探寻参数估计的数值方法,并总结出EM算法的一般过程。基于matlab编程可视化EM算法下的GMM模型参数更新过程,对比MLE目标函数和EM迭代目标函数,分析EM算法的内涵思想并结合图形进行直观展示,并且挖掘其中蕴含的思政元素,在知识传授的同时实现价值塑造。Expectation maximization (EM) algorithm is a core algorithm in statistics and also a key and difficult point in the teaching process of modern mathematical statistics courses in our school. The paper adopts a case-based and heuristic teaching method, taking the Gaussian Mixture Model (GMM) based bearing degradation stage division problem as an example, guiding students to discover the difficulties of maximum likelihood estimation (MLE) in the latent variable model, designing a problem chain to inspire students to explore numerical methods for parameter estimation, and summarizing the general process of EM algorithm. Based on Matlab programming, the parameter update process of GMM based on EM algorithm is visualized. Comparing the MLE objective function and EM iteration objective function, the intrinsic thought of EM algorithm is analyzed and visually displayed with graphics. The ideological and political elements are also explored, so as to achieve value shaping while knowledge transmission.展开更多
遥感图像在采集时,由于受到各种因素干扰,会严重影响图像的视觉效果,进而影响后续处理的准确性。因此,对遥感图像的噪声进行准确地建模是解决遥感图像噪声问题的关键。编码噪声分布最常选择是高斯分布、拉普拉斯分布和高斯混合分布,但...遥感图像在采集时,由于受到各种因素干扰,会严重影响图像的视觉效果,进而影响后续处理的准确性。因此,对遥感图像的噪声进行准确地建模是解决遥感图像噪声问题的关键。编码噪声分布最常选择是高斯分布、拉普拉斯分布和高斯混合分布,但它们总是与现实世界的遥感图像噪声不相容。考虑到遥感图像同时存在对称和非对称的噪声分布,本文在高斯混合分布基础上,引入了非对称参数,构建了一个基于非对称高斯混合分布模型(AMoG)的遥感图像去噪算法。该算法使用低秩矩阵分解将遥感图像近似为两个因子矩阵的乘积。对于模型的参数,使用了EM算法进行迭代更新。在合成数据集和真实数据集上的大量实验结果表明,该模型在PSNR、SSIM、FSIM、ERGA、SAM五种评价指标上均表现良好,表明了该算法在遥感图像去噪方面具有一定的优越性。Remote sensing images are often subject to various interferences during acquisition, which seriously affects the visual effect of the images, and then affects the accuracy of subsequent processing. Therefore, accurate modeling of the noise of remote sensing images is the key to solving the noise problem of remote sensing images. The most common choices for coded noise distributions are Gaussian, Laplace, and Gaussian mixtures, but they are always incompatible with real-world remote sensing image noise. Considering that there are both symmetrical and asymmetric noise distribution in remote sensing images, this paper introduces asymmetric parameters on the basis of Gaussian mixed distribution, and constructs a remote sensing image denoising algorithm based on asymmetric Gaussian mixed distribution model (AMoG). The algorithm uses low-rank matrix factorization to approximate the remote sensing image as the product of two-factor matrices. For the parameters of the model, the EM algorithm was used for iterative update. A large number of experimental results on synthetic datasets and real datasets show that the model performs well in five evaluation indexes: PSNR, SSIM, FSIM, ERGA and SAM, indicating that the algorithm has certain advantages in remote sensing image denoising.展开更多
图像在采集和传输过程中常常会受到噪声的干扰,这会严重影响图像的质量。因此,高效的图像去噪方法成为图像处理领域的重要研究课题。对图像噪声进行精准建模是提升图像去噪性能的关键步骤,本文针对这一问题,提出了一种基于广义高斯混合...图像在采集和传输过程中常常会受到噪声的干扰,这会严重影响图像的质量。因此,高效的图像去噪方法成为图像处理领域的重要研究课题。对图像噪声进行精准建模是提升图像去噪性能的关键步骤,本文针对这一问题,提出了一种基于广义高斯混合模型的低秩矩阵分解方法。通过假设噪声服从广义高斯混合分布,精确地刻画复杂的噪声特性,并通过低秩矩阵分解捕获数据的主要结构特征。为优化模型参数,采用期望最大化算法进行迭代更新。在合成数据和真实图像数据集上的实验表明,该模型优于本文其他对比模型,表明该算法在图像去噪方面有一定的优势。Images are often disturbed by noise during acquisition and transmission, which can seriously affect the quality of images. Therefore, efficient image denoising methods have become an important research topic in the field of image processing. Accurate modeling of image noise is a key step to improve the performance of image denoising, and this paper proposes a low-rank matrix decomposition method based on the generalized Gaussian mixture model to address this problem. By assuming that the noise obeys a generalized Gaussian mixture distribution, the complex noise characteristics are accurately portrayed, and the main structural features of the data are captured by the low-rank matrix decomposition. To optimize the model parameters, an expectation maximization algorithm is used for iterative updating. Experiments on synthetic data and real image datasets show that the model outperforms other comparative models in this paper, indicating that the algorithm has some advantages in image denoising.展开更多
文摘EM (Expectation Maximization)算法是统计学中的核心算法,也是本校近代数理统计课程教学过程中的一个重难点。论文采用案例式、启发式、研讨式教学方法,以基于高斯混合模型(GMM)的轴承退化阶段划分问题为例,引导学生发现隐变量模型极大似然估计(MLE)存在的困难,设计问题链启发学生探寻参数估计的数值方法,并总结出EM算法的一般过程。基于matlab编程可视化EM算法下的GMM模型参数更新过程,对比MLE目标函数和EM迭代目标函数,分析EM算法的内涵思想并结合图形进行直观展示,并且挖掘其中蕴含的思政元素,在知识传授的同时实现价值塑造。Expectation maximization (EM) algorithm is a core algorithm in statistics and also a key and difficult point in the teaching process of modern mathematical statistics courses in our school. The paper adopts a case-based and heuristic teaching method, taking the Gaussian Mixture Model (GMM) based bearing degradation stage division problem as an example, guiding students to discover the difficulties of maximum likelihood estimation (MLE) in the latent variable model, designing a problem chain to inspire students to explore numerical methods for parameter estimation, and summarizing the general process of EM algorithm. Based on Matlab programming, the parameter update process of GMM based on EM algorithm is visualized. Comparing the MLE objective function and EM iteration objective function, the intrinsic thought of EM algorithm is analyzed and visually displayed with graphics. The ideological and political elements are also explored, so as to achieve value shaping while knowledge transmission.
文摘遥感图像在采集时,由于受到各种因素干扰,会严重影响图像的视觉效果,进而影响后续处理的准确性。因此,对遥感图像的噪声进行准确地建模是解决遥感图像噪声问题的关键。编码噪声分布最常选择是高斯分布、拉普拉斯分布和高斯混合分布,但它们总是与现实世界的遥感图像噪声不相容。考虑到遥感图像同时存在对称和非对称的噪声分布,本文在高斯混合分布基础上,引入了非对称参数,构建了一个基于非对称高斯混合分布模型(AMoG)的遥感图像去噪算法。该算法使用低秩矩阵分解将遥感图像近似为两个因子矩阵的乘积。对于模型的参数,使用了EM算法进行迭代更新。在合成数据集和真实数据集上的大量实验结果表明,该模型在PSNR、SSIM、FSIM、ERGA、SAM五种评价指标上均表现良好,表明了该算法在遥感图像去噪方面具有一定的优越性。Remote sensing images are often subject to various interferences during acquisition, which seriously affects the visual effect of the images, and then affects the accuracy of subsequent processing. Therefore, accurate modeling of the noise of remote sensing images is the key to solving the noise problem of remote sensing images. The most common choices for coded noise distributions are Gaussian, Laplace, and Gaussian mixtures, but they are always incompatible with real-world remote sensing image noise. Considering that there are both symmetrical and asymmetric noise distribution in remote sensing images, this paper introduces asymmetric parameters on the basis of Gaussian mixed distribution, and constructs a remote sensing image denoising algorithm based on asymmetric Gaussian mixed distribution model (AMoG). The algorithm uses low-rank matrix factorization to approximate the remote sensing image as the product of two-factor matrices. For the parameters of the model, the EM algorithm was used for iterative update. A large number of experimental results on synthetic datasets and real datasets show that the model performs well in five evaluation indexes: PSNR, SSIM, FSIM, ERGA and SAM, indicating that the algorithm has certain advantages in remote sensing image denoising.
文摘图像在采集和传输过程中常常会受到噪声的干扰,这会严重影响图像的质量。因此,高效的图像去噪方法成为图像处理领域的重要研究课题。对图像噪声进行精准建模是提升图像去噪性能的关键步骤,本文针对这一问题,提出了一种基于广义高斯混合模型的低秩矩阵分解方法。通过假设噪声服从广义高斯混合分布,精确地刻画复杂的噪声特性,并通过低秩矩阵分解捕获数据的主要结构特征。为优化模型参数,采用期望最大化算法进行迭代更新。在合成数据和真实图像数据集上的实验表明,该模型优于本文其他对比模型,表明该算法在图像去噪方面有一定的优势。Images are often disturbed by noise during acquisition and transmission, which can seriously affect the quality of images. Therefore, efficient image denoising methods have become an important research topic in the field of image processing. Accurate modeling of image noise is a key step to improve the performance of image denoising, and this paper proposes a low-rank matrix decomposition method based on the generalized Gaussian mixture model to address this problem. By assuming that the noise obeys a generalized Gaussian mixture distribution, the complex noise characteristics are accurately portrayed, and the main structural features of the data are captured by the low-rank matrix decomposition. To optimize the model parameters, an expectation maximization algorithm is used for iterative updating. Experiments on synthetic data and real image datasets show that the model outperforms other comparative models in this paper, indicating that the algorithm has some advantages in image denoising.
