高噪声图像的结构性缺失低秩矩阵重建算法  

Reconstruction algorithm for structurally deficient low-rank matrix of high-noise images

作　　者：张虹 左鑫兰 黄瑶 ZHANG Hong;ZUO Xinlan;HUANG Yao(College of Computer and information Technology,China Three Gorges University,Yichang 443002,China)

机构地区：[1]三峡大学计算机与信息学院,湖北宜昌443002

出　　处：《哈尔滨工程大学学报》2021年第3期407-412,共6页Journal of Harbin Engineering University

基　　金：湖北省自然科学基金项目(2019CFB215).

摘　　要：为了提高图像信噪比和结构性缺失低秩矩阵重建精度,本文提出基于重加权的高噪声图像的结构性缺失低秩矩阵重建算法。利用中值滤波、阈值处理以及小波系数法对高频子带图像中的脉冲噪声进行处理。利用小波逆变换获取恢复图像,实现高噪声图像初步处理,构建低秩与稀疏先验下结构性缺失矩阵重建模型。根据低秩先验和稀疏先验对重建矩阵进行约束,并通过重加权策略强化低秩与先验性,增强矩阵重建精确性。在重加权策略架构下,实现模型约束向无约束子问题的转化,并通过交替方向法实现模型求解。实验结果表明:该方法可实现结构性缺失低秩矩阵的高精度重建,峰值信噪比高达29.05 dB,平均绝对误差低于18。证明该方法有较好的图像降噪性能,提高了结构性缺失低秩矩阵重建精度。In order to improve the image signal-to-noise ratio(SNR)and the reconstruction accuracy of the structurally deficient,low-rank matrix,a reconstruction algorithm for such a matrix is proposed in this paper based on weighted high-noise images.Median filtering,threshold processing,and wavelet coefficient method are used to process the impulse noise in high frequency subband images.The inverse wavelet transform is used to obtain the restored image and realize the preliminary processing of the high-noise image.The reconstruction model of the structurally deficient matrix is constructed under low rank and sparse prior.The reconstruction matrix is constrained according to low rank and sparse prior.A heavy weighting strategy is used to enhance the low rank and priori,and increase the accuracy of matrix reconstruction.In the framework of this strategy,the model constraints are transformed into unconstrained subproblems.The model is solved by an alternating direction method.Experimental results show that this method can achieve high-precision reconstruction of the structurally deficient low-rank matrix.The peak SNR reaches up to 29.05 dB,and the average absolute error is less than 18.It is proved that this method has better image denoising performance and improves the reconstruction accuracy of the structurally deficient low-rank matrix.

关 键 词：高噪声图像 邻域平均法 结构性缺失 低秩矩阵 重加权 拉格朗日函数 灰度值 高斯噪声 脉冲噪声 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]