基于偏微分方程的混合噪声去噪研究

针对目前图像去噪方法存在的主要缺陷是仅适用于单一噪声的滤除, 无法解决图像混合噪声去噪的问题, 提出一种加权混合噪声模型, 建立其能量泛函表达式, 利用变分法获得其欧拉—拉格朗日方程并给出其显式差分迭代求解算法。通过对其数值算法的改进, 不仅提高了该模型数值算法的速度和稳定性, 而且在一定程度上避免了降噪后图像的阶梯效应。仿真实验表明, 加权混合噪声去噪算法在去除混合噪声的同时更好地保留了图像的细节信息, 其降噪性能相比现有方法有一定程度的改善。

Mixed noise denoised based on partial differential equation

As the most major drawback of the present image denoising methods is only appropriate for the single noise removal and can not solve the mixed denoising problem. This paper presented a weighting mixed noise model and established the energy functional expression of the model, then used variational method to get the Euler-Lagrange equation of the model. Furthermore, it proposed an improved iterative algorithm to solve the proposed model based on explicit difference iteration regularization method. The improved numerical algorithm can not only enhance the speed and the stability of numerical algorithm, but also avoid the staircase effect of the image denoising in some way. The simulation results show that the proposed model can effectively smooth the noises and preserve the edge and fine detail information properly, while comparing with the traditional algorithm, noise reduction performance is improved at some level.