基于Shannon-Cosine小波精细积分法的壁画降噪修复方法

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。

Mural image de-noising based on Shannon-Cosine wavelet precise integration method

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.