在遥感图像的拍摄和传输过程中,会产生大量的噪声,高斯噪声和椒盐噪声是较为常见的两种噪声,目前的去噪算法对于这类混合噪声的去除普遍存在边缘模糊等问题。针对此问题,文章提出了一种新的基于组稀疏混合模型的遥感图像混合噪声的去除...在遥感图像的拍摄和传输过程中,会产生大量的噪声,高斯噪声和椒盐噪声是较为常见的两种噪声,目前的去噪算法对于这类混合噪声的去除普遍存在边缘模糊等问题。针对此问题,文章提出了一种新的基于组稀疏混合模型的遥感图像混合噪声的去除方法,首先通过双边矩阵乘法提高块组的稀疏性,然后通过块组独立这一假设提出了基于块组的混合噪声去噪框架,接着对辅助变量、估计的图像、椒盐噪声分别进行最小化问题的优化求解,最后通过聚合块组得到去噪后的图像。实验结果表明,本文的算法能够有效地去除遥感图像中的高斯噪声和椒盐噪声,相对于其他传统方法具有更高的PSNR、SSIM以及FSIM数值。In the process of capturing and transmitting remote-sensing images, a large amount of noise is generated. Gaussian noise and salt-and-pepper noise are two common types of noise. Current denoising algorithms generally have problems with edge blurring when removing such mixed noise. To address this problem, we propose a new method based on a group sparse mixed model to remove mixed noise in remote sensing images. Firstly, the sparsity of patch groups is improved through bilateral matrix multiplication. Then, a patch group-based mixed noise denoising framework is proposed based on the assumption of patch group independence. Then, the auxiliary variables, estimated images, and salt and pepper noise are optimized and solved separately. Finally, the denoised image is obtained by aggregating patch groups. Experimental results show that the algorithm in this paper can effectively remove Gaussian noise and salt-and-pepper noise in remote sensing images and has higher values of PSNR, SSIM, and FSIM compared with several popular algorithms.展开更多
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
文摘在遥感图像的拍摄和传输过程中,会产生大量的噪声,高斯噪声和椒盐噪声是较为常见的两种噪声,目前的去噪算法对于这类混合噪声的去除普遍存在边缘模糊等问题。针对此问题,文章提出了一种新的基于组稀疏混合模型的遥感图像混合噪声的去除方法,首先通过双边矩阵乘法提高块组的稀疏性,然后通过块组独立这一假设提出了基于块组的混合噪声去噪框架,接着对辅助变量、估计的图像、椒盐噪声分别进行最小化问题的优化求解,最后通过聚合块组得到去噪后的图像。实验结果表明,本文的算法能够有效地去除遥感图像中的高斯噪声和椒盐噪声,相对于其他传统方法具有更高的PSNR、SSIM以及FSIM数值。In the process of capturing and transmitting remote-sensing images, a large amount of noise is generated. Gaussian noise and salt-and-pepper noise are two common types of noise. Current denoising algorithms generally have problems with edge blurring when removing such mixed noise. To address this problem, we propose a new method based on a group sparse mixed model to remove mixed noise in remote sensing images. Firstly, the sparsity of patch groups is improved through bilateral matrix multiplication. Then, a patch group-based mixed noise denoising framework is proposed based on the assumption of patch group independence. Then, the auxiliary variables, estimated images, and salt and pepper noise are optimized and solved separately. Finally, the denoised image is obtained by aggregating patch groups. Experimental results show that the algorithm in this paper can effectively remove Gaussian noise and salt-and-pepper noise in remote sensing images and has higher values of PSNR, SSIM, and FSIM compared with several popular algorithms.
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.
