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Shannon-Cosine Wavelet Precise Integration Method for Locust Slice Image Mixed Denoising
Mathematical Problems in Engineering ( IF 1.430 ) Pub Date : 2020-07-14 , DOI: 10.1155/2020/4989735 Haihua Wang 1, 2 , Xinxin Zhang 1, 2 , Shuli Mei 1, 2
Mathematical Problems in Engineering ( IF 1.430 ) Pub Date : 2020-07-14 , DOI: 10.1155/2020/4989735 Haihua Wang 1, 2 , Xinxin Zhang 1, 2 , Shuli Mei 1, 2
Affiliation
A novel denoising method for removing mixed noise from locust slice images is proposed by means of Shannon-cosine wavelet and the nonlinear variational model for the image processing. This method includes two parts that are the sparse representation of the slice images and the novel numerical algorithm for solving the variation model on image denoising based on the sparse representation. In the first part, a parametric Shannon-cosine wavelet function is introduced to construct the multiscale wavelet transform matrix, which is applied to represent the slice images sparsely by adjusting the parameters adaptively based on the texture of the locust slice images. By multiplying the matrix with the signal, the multiscale wavelet transform coefficients of the signal can be obtained at one time, which can be used to identify the salt-and-pepper noises in the slice images. This ensures that the salt-and-pepper noise points are kept away from the sparse representation of the slice images. In the second part, a semianalytical method on solving the system of the nonlinear differential equations is constructed based on the sparse representation of the slice images, which is named the sparse wavelet precise integration method (SWPIM). Substituting the sparse representation of the slice images into the Perona–Malik model which is the famous edge-preserving smoothing model for removing the Gaussian noises of the biomedical images, a system of nonlinear differential equations is obtained, whose scale is far smaller than the one obtained by the difference method. The numerical experiments show that both the values of SSIM and PSNR of the denoised locust slice images are better than the classical methods besides the algorithm efficiency.
中文翻译:
香农-余弦小波精确积分的蝗虫切片图像混合去噪
提出了一种利用香农余弦小波和非线性变分模型对蝗虫切片图像进行去噪的去噪方法。该方法包括切片图像的稀疏表示和解决基于稀疏表示的图像去噪变化模型的新型数值算法两部分。在第一部分中,引入参数香农-余弦小波函数构造多尺度小波变换矩阵,该矩阵通过基于蝗虫切片图像的纹理自适应地调整参数来稀疏地表示切片图像。通过将矩阵与信号相乘,可以一次获得信号的多尺度小波变换系数,可以用来识别切片图像中的椒盐噪声。这确保了盐和胡椒的噪声点远离切片图像的稀疏表示。在第二部分中,基于切片图像的稀疏表示构造了一种求解非线性微分方程组的半解析方法,称为稀疏小波精确积分方法(SWPIM)。将切片图像的稀疏表示代入著名的边缘保留平滑模型Perona-Malik模型中,该模型用于消除生物医学图像的高斯噪声,从而获得了一个非线性微分方程组,其规模远远小于一个通过差异法获得。
更新日期:2020-07-14
中文翻译:
香农-余弦小波精确积分的蝗虫切片图像混合去噪
提出了一种利用香农余弦小波和非线性变分模型对蝗虫切片图像进行去噪的去噪方法。该方法包括切片图像的稀疏表示和解决基于稀疏表示的图像去噪变化模型的新型数值算法两部分。在第一部分中,引入参数香农-余弦小波函数构造多尺度小波变换矩阵,该矩阵通过基于蝗虫切片图像的纹理自适应地调整参数来稀疏地表示切片图像。通过将矩阵与信号相乘,可以一次获得信号的多尺度小波变换系数,可以用来识别切片图像中的椒盐噪声。这确保了盐和胡椒的噪声点远离切片图像的稀疏表示。在第二部分中,基于切片图像的稀疏表示构造了一种求解非线性微分方程组的半解析方法,称为稀疏小波精确积分方法(SWPIM)。将切片图像的稀疏表示代入著名的边缘保留平滑模型Perona-Malik模型中,该模型用于消除生物医学图像的高斯噪声,从而获得了一个非线性微分方程组,其规模远远小于一个通过差异法获得。