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浙江大学学报（理学版）
浙江大学学报（理学版）  2019, Vol. 46 Issue (3): 279-287    DOI: 10.3785/j.issn.1008-9497.2019.03.003
文化计算     
基于Shannon-Cosine小波精细积分法的壁画降噪修复方法
李丽1, 高若婉1, 梅树立1, 赵海英2
1.中国农业大学 信息与电气工程学院，北京 100083
2.北京邮电大学 世纪学院, 北京 102613
Mural image de-noising based on Shannon-Cosine wavelet precise integration method
Li LI1, Ruowan GAO1, Shuli MEI1, Haiying ZHAO2
1.College of Information and Electrical Engineer, China Agricultural University, Beijing 100083, China
2.Mobile Media and Cultural Computing Key Laboratory of Beijing, Century College, Beijing University of Post & Telecommunication, Beijing 102613, China
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摘要： 为修复受破损且噪声点众多的壁画图像，提出了用偏微分方程（partial differential equation，PDE）扩散的方法对图像进行降噪修复。针对PDE法求解精度较低的问题，提出了一种Shannon-Cosine小波精细积分法，运用小波数值方法对偏微分方程进行离散处理，降低其方程组规模，并采用精细积分法求解，有效提高了计算速度。试验结果表明，采用该算法对受损壁画降噪处理后，视觉上，图像边界更清晰，且噪声点得到有效减少，达到了保边降噪的效果，更符合人眼的视觉效果；客观上，与中值滤波、均值滤波和维纳滤波方法相比，采用本算法处理后的图像其PSNR值和SSIM值均最大。因此，运用Shannon-Cosine小波精细积分法求解图像的PDE模型是可行的，取得了较好的图像降噪效果。
关键词： 壁画;  降噪;  小波精细积分法;  偏微分方程    
Abstract: Ancient murals are precious historical and cultural heritages of China. In order to repair the damaged mural images, a method of partial differential equation (PDE) diffusion is proposed to denoise these images. To solve the PDE equation, the method of difference is usually adopted, but the accuracy of the method is not enough. To solve this problem, we introduce a Shannon-Cosine wavelet precise integration method. It adopts the wavelet numerical method to discretize the partial differential equation so as to reduce the size of the equation set. The precise integration method is then employed to solve the ordinary differential equations, which can effectively improve the calculation speed. Experimental results show that the de-noised image obtained by the proposed algorithm has less residual noise and clearer textures in comparison with other algorithms. Two common de-noise evaluation criteria of image were adopted, i.e. PSNR and structural similarity image measurement (SSIM), which measured the degree of image distortion and similarity between the processed and the original image. Compared with median filtering, mean filtering and Wiener filtering, the PSNR and SSIM values of the image processed by this algorithm are the largest.In conclusion, the proposed algorithm is feasible and effective for de-noising murals image.
Key words: murals    image de-noising    wavelet precise integration method    partial differential equations
收稿日期: 2019-01-19 出版日期: 2019-05-25
CLC:  TP391.41  
基金资助: 国家自然科学基金资助项目(61871380)； 基金项目:北京市自然科学基金资助项目(4172034).
通讯作者: ORCID： http：//orcid.org/0000-0002-0240-4573 ，通信作者:E-mail：zhaohaiying@bupt.edu.cn.     E-mail: zhaohaiying@bupt.edu.cn.
作者简介: 李丽(1963—)，ORCID:http://orcid.org/0000-0002-6521-7740 ，女，博士，教授，主要从事计算机图形图像处理技术研究.
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引用本文:

李丽, 高若婉, 梅树立, 赵海英. 基于Shannon-Cosine小波精细积分法的壁画降噪修复方法[J]. 浙江大学学报（理学版）, 2019, 46(3): 279-287.

Li LI, Ruowan GAO, Shuli MEI, Haiying ZHAO. Mural image de-noising based on Shannon-Cosine wavelet precise integration method. Journal of Zhejiang University (Science Edition), 2019, 46(3): 279-287.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2019.03.003    或    https://www.zjujournals.com/sci/CN/Y2019/V46/I3/279

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