中文摘要：

讨论了光学图像中同时存在噪声与模糊时的对比度增强问题。构造了一种基于边缘定向扩散的各向异性非线性扩散方程来作为图像的光滑约束项，并根据模糊后的图像在边缘处相对清晰图像具有较大误差的事实，构造增强图像与原图像之间的非均匀逼近项，将此两项通过正则化参数联系起来，得到了一种图像对比度增强的正则化模型，并利用Euler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。该模型能在抑制噪声的同时增强图像的边缘，在模型的解算上也不存在大型矩阵的存储与运算问题。数值计算结果表明，新方法适合于多种形式的模糊和不同程度的噪声污染，相对现有方法具有更好的边缘锐化能力和更高的清晰度，峰值信噪比比现有方法提高了1～2dB，边缘保护指数也比现有方法有较大提高。

英文摘要：

The contrast enhancement of blurred and noised image is discussed. It constructs an edge-directed anisotropic nonlinear diffusion to constrain the smoothness of the image, and constructs an unhomogeneous approach constraint according to the distribution of the imaging error. A regularization model for contrast enhancement is obtained by combining these two constraints through a regularization parameter. This regularization model can turn to be an anisotropic nonlinear diffusion by solving its Euler equation, which can be solved fast. The new model can reduce noise and enhance edge at the same time, and can avoid the computation of huge matrix. Numerical results showed that the new model was suited for different blur and a wide range of noise levels, and could get sharper edges and clearer images than known methods, and it also had one or two dB higher peak signal to noise ratio （PSNR） and higher edge kept index （EKI） than known models.