摘要
对3类常见正交基函数的稀疏变换即离散余弦转换(DCT)、离散小波变换(DWT)、奇异值分解(SVD)进行研究,在构建基函数的基本稀疏表示的模型基础上,以灰度图像受到高斯噪声干扰为例,建立了3类含高斯噪声的稀疏变换模型;利用MATLAB中的块操作实现对图像的稀疏分解,得到图像完整的稀疏特征矩阵,过滤其中的表现为高斯噪声的高频分量,通过稀疏反变换模型重构代表图像最主要结构的低频分量,最终获得去噪图像。结果表明,DWT算法的综合去噪性能最优,SVD算法在低标准偏差下去噪图像画面质量最高,而DCT算法则在高标准偏差下噪点消除能力最佳。
Three kinds of common orthogonal basis functions transform(discrete cosine transformation(DGT),discrete wavelet transform(DWT)and singular value decomposition(SVD))were studied.On the basis of building sparse representation model for primary function,and taking gray image with Gaussian noise interference as example,three categories sparse transform model with Gaussian noise were established.Using block operation in MATLAB to realize the image sparse decomposition,the complete sparse feature matrix of images was obtained.Filtering high frequency components in the form of Gaussian noise,the de-noised image was obtained by using sparse transformation model to reconstruct low frequency component of the main structure of the image.The results show that the integrated noise reduction performance of DWT is the best,the de-noised image picture quality of SVD is the highest under the lower standard deviation,and the noise elimination capacity of DGT is the best under the high standard deviation.
作者
赵伟良
刘世豪
ZHAO Weiliang;LIU Shihao(College of Mechanical and Electrical Engineering, Hainan University, Haikou 570228 , China)
出处
《济南大学学报（自然科学版）》
CAS
北大核心
2018年第2期89-95,共7页
Journal of University of Jinan(Science and Technology)
基金
国家自然科学基金项目(51405115)
关键词
图像去噪
稀疏变换
去噪质量评价
离散余弦变换
离散小波变换
奇异值分解
image de-noising
sparse transform
de-noising quality evaluation
discrete cosine transform
discrete wavelet transform
singular value decompsition
