基于滤波方法和矩阵低秩稀疏分解的遥感图像去噪算法

Remote Sensing Image Denoising Algorithm Based on Filtering Method and Matrix Low-Rank Sparse Decomposition

摘要: 针对遥感图像在形成、传输和处理过程中产生的椒盐噪声问题，设计了一种结合中值滤波、矩阵低秩分解与导向滤波的遥感图像去噪算法。给定含噪图像，该算法首先对图像进行有互相重叠像素的分块处理，利用非精确增广拉格朗日乘子法求解分块后图像所对应的矩阵低秩分解模型，得到稀疏图像和噪声图像，然后利用中值滤波算法对给定的含噪图像进行处理，对处理后的图像与稀疏图像相加求和，将结果作为引导图像，含噪图像作为输入图像，利用导向滤波算法得到保留遥感图像细节信息的复原图像。通过与其它方法对比，证明了本文方法的有效性。

Abstract: In view of the salt and pepper noise generated during the formation, transmission and processing of remote sensing images, a remote sensing image denoising algorithm combining median filtering, matrix low-rank decomposition and guided filtering is designed. Given a noisy image, the algorithm first divides the image into overlapped patches, and uses the inexact augmented Lagrange multiplier method to solve the matrix low-rank decomposition model of the block image to obtain the sparse image and the noise image. Then the algorithm uses the median filter to process the given noisy image, the sum of the denoised image and the sparse image is used as the guide image, the noisy image is used as input image, and the restored image that retains the details of the remote sensing image is obtained by using the guide filter. Compared with several existing methods, the effectiveness of the proposed method is effectively proved.