基于B-样条二进小波变换的一种改进图像复原方法  

Image Restoration Method Based on B-Spline Dyadic Wavelet Transform

作　　者：马瑞瑞 王刚[1] 张静[1] 董永秀 

机构地区：[1]新疆师范大学数学科学学院,新疆 乌鲁木齐 [2]新疆克拉玛依南湖小学,新疆 克拉玛依

出　　处：《理论数学》2022年第2期309-315,共7页Pure Mathematics

摘　　要：传统的图像复原的方法会造成图像细节的丢失,且去噪效果一般,结合二进小波变换、高斯滤波和阈值函数去噪的优点,我们提出了一种基于B-样条二进小波变换的图像恢复方法。本文利用小波变换,用新构造的B-样条二进小波滤波器将方差为0.005的高斯噪声图像分解三次,分解得到的每一层高频系数分别使用传统的软阈值模型进行阈值去噪,仅对第一层分解得到的低频系数使用二维高斯滤波器进行去噪,接着,将处理后的高频低频系数利用小波逆变换从第三层重构到第二层,从第二层重构到第一层,从第一层重构到第零层,最后得到复原图像,结果显示本文得到的去噪图像充分保留了原图像的细节,人物的边缘,物体的边缘都能很好地被人眼观察到,具有很好的实用性。The traditional image restoration method will cause the loss of image details, and the denoising effect is general. Combining the advantages of binary wavelet transform, Gaussian filtering and threshold function denoising, we propose a B-spline binary wavelet transform based method—Image restoration method. In this paper, the wavelet transform is used to decompose the Gaussian noise image with a variance of 0.005 three times with the newly constructed B-spline binary wavelet filter. Only the low-frequency coefficients decomposed in the first layer are denoised using a two-dimensional Gaussian filter, and then the processed high-frequency and low-frequency coefficients are reconstructed from the third layer to the second layer using inverse wavelet transform, and the second layer is repeated from the second layer. The first layer is constructed, reconstructed from the first layer to the zeroth layer, and finally the restored image is obtained. The results show that the denoised image obtained in this paper fully retains the details of the original image, and the edges of characters and objects can be well observed by the human eye, it has good practicality.

关 键 词：B-样条二进小波变换 阈值去噪 高斯滤波 图像复原 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]