一种基于卷积运算与全变分模型的图像去噪方法

梯度模值较易受到外界影响，导致全变分模型在大噪声点处往往不能很好地消除噪声，从而产生阶梯效应。针对该问题，提出了一种基于卷积运算与全变分模型的图像去噪方法。首先，针对以扩散形式获得的图像像素点进行卷积运算，利用滤波去噪降低大噪声点的灰度值；其次，以能量泛函形式构建图像全变分模型，并求解泛函对应的拉格朗日方程极小值来实现图像去噪；最后，将去噪后图像作为双边滤波算法的引导图像进行二次去噪，从而进一步提升图像去噪质量。仿真实验结果表明，与经典方法相比，该模型对去噪过程中的阶梯效应问题具有较好的处理效果。

An Image Denoising Method Based on Convolution Operation and Full Variational Model

The gradient mode value is easy to be influenced by the outside world,which results in the problem that the total variational model cannot eliminate the noise well at the big noise point,thus producing the step effect.To solve this problem,an image denoising method based on convolution operation and full variational model is proposed.Firstly,the convolution operation is carried out for the image pixel points obtained in the form of diffusion.Secondly,the full variational model of image is constructed in the form of energy functional,and the image denoising is realized by solving the minimum value of Lagrange equation corresponding to the functional.Finally,the de-noised image is used as the guide image of the bilateral filtering algorithm for secondary de-noising,so as to further improve the image de-noising quality.The simulation results show that the model is better than the classical method in dealing with the step effect in the denoising process.