基于小波变换的压缩全变分图像降噪模型
Wavelet-Based Compressive Total Variation Model for Image Denoising
DOI: 10.12677/JISP.2022.113010, PDF,   
作者: 王 迪, 李万社：陕西师范大学数学与统计学院，陕西 西安
关键词: 图像降噪；低秩；压缩全变分；Image Denoising； Low-Rank； Compressive Total Variation
摘要: 从被噪声污染的图像(即观测图像)中恢复原始图像是图像处理的主要任务之一，原始图像矩阵在小波变换域其近似系数矩阵是低秩的，并且对应的梯度变换矩阵是低秩且稀疏的，基于此先验知识，对观测图像的近似系数矩阵使用压缩全变分降噪模型即通过极小化一个含有保真项和正则化项的能量泛函实现降噪，利用小波逆变换重构图像，可实现观测图像降噪。
Abstract: It is one of the main tasks of image processing to recover the original image from the noise-polluted image (observed image). The approximate coefficient matrix of the original image matrix in the wavelet transform domain is low-rank, and the corresponding gradient transform matrix is low-rank and sparse. Based on this prior knowledge, the compressed total variation image denoising model is used for the approximate coefficient matrix of the observed image, that is, the denoising of the observed image is realized by minimising an energy functional containing the fitting term and regularization term, and the image is reconstructed by using the inverse wavelet transform.
文章引用：王迪, 李万社. 基于小波变换的压缩全变分图像降噪模型[J]. 图像与信号处理, 2022, 11(3): 85-91. https://doi.org/10.12677/JISP.2022.113010

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