Abstract: One of the negative effects of denoising method with second-order nonlinear diffusion equation is the staircase effect, which is difficult to be avoided. The image distortion would be caused more or less though the staircase effect can be reduced by the existed gradient fidelity term. A new exponent adapted gradient fidelity term and a gradient adapted exponential function are put forward by improving the exciting methods and the exponential function property in this paper. It is shown that the exponent adapted gradient fidelity term is able to enhance the denoising ability and get better visual results by the experiments.

Key words: staircase effect, gradient information, nonlinear diffusion equation, exponent function, image denoising

摘要： 阶梯效应是利用二阶非线性扩散方程进行去噪很难避免的负面效应之一。已有的梯度保真项虽然能够一定程度上缓解阶梯效应，但也会造成不同程度的图像失真，根据已有方法与指数函数的性质提出了一种新的指数自适应的梯度保真项并且构造了自适应图像梯度的指数函数，在保证削弱阶梯效应的基础上可以得到更好的去噪效果与视觉效果，并且能够适应扩散项。实验证明，指数自适应梯度保真项可以明显减弱阶梯效应，保留更多纹理细节，并且得到与已有方法相比更高的信噪比。

关键词: 阶梯效应, 梯度信息, 非线性扩散方程, 指数函数, 图像去噪