基于边缘定向扩散方程的图像复原方法

讨论了光学图像中同时存在噪声与模糊时的复原问题。采用一种能根据边缘方向自适应选取扩散系数的各向异性扩散方程来约束复原后的图像的光滑性质，将其和图像复原模型一起使用，得到了一种图像复原的正则化模型，并利用Eluer方程将该模型转换成一种可以快速求解的各向异性非线性扩散模型。在光滑性约束项的构造上，构造了一种基于边缘定向扩散的各向异性张量型扩散方程，能有效地根据边缘的方向确定是增强边缘还是滤除噪声。相比图像复原的迭代正则化方法，新方法能在复原图像的同时有效地抑制噪声，并有效地减轻边缘处的振铃效应。数值计算结果表明，新方法在整幅图像的复原效果上明显强于迭代正则化方法，尤其在对背景噪声的抑制上效果更明显，峰值信噪比（PSNR）也比迭代正则化方法平均提高了约2dB。

Image Restoration Based on Edge-directed Diffusion

The restoration of blurred and noised image was investigated.Since image restoration is an ill-posed problem,we construct and anisotropic nonlinear diffusion based cost function to constrain the smoothness of deblurred image.By combining the smoothness constraint with the restoration model by a regularization parameter,we get a nonlinear diffusion based regularization model for image restoration.Solve the regularization model by its Euler equation,and then the regularization model turns to be an anisotropic nonlinear diffusion equation.To construct a valid smoothness constraint,an edge-directed tensor diffusion is used,which can automatically select to denoise or to enhance edge according to the direction of edges.Compared with traditional iterative regularization model,the new model can restore image effectively and reduce noise simultaneously,especially on the control of background noise.The peak signal to noise ratio (PSNR) of new model is about 2 dB higher than traditional iterative regularization model.