摘要
针对现有偏微分方程复原模型存在的弱点,提出了一种改进的全有界变差四阶偏微分方程图像复原模型,证明了模型的适定性。由于模型的Euler-Lagrange方程是非线性偏微分方程,利用分裂Bregman迭代算法,将其分解为三个线性子问题,结合Gauss-Seidel迭代方法得到了数值解。从实验结果和客观评价上看,上述模型和算法在对图像复原的过程中,与ROF模型和TBV_ROF模型相比较,峰值信噪比和平均结构相似度都有明显的提高。模型在复原的同时,能够很好地保持原始图像上的边缘和纹理特征,复原能力优于ROF模型和TBV_ROF模型。
For the weaknesses of traditional image restoration models of partial differential equation,a total norm regularization image restoration model of fourth-order PDE was presented and it＇s well-posed property was proved in this paper. Due to the Euler-Lagrange equation of the model is nonlinear PDE,the equation was decomposed to three linear problems using split Bregman iteration algorithms. This paper obtained the numerical solutions of the model combined with the Gauss-Seidel iteration method. Then from the objective evaluation and the experimental data,the PSNR and MSSIM have obviously increased compared with the ROF model and TBV_ROF modelin restoration processing. The new model is able to protect the edge and texture of the original imageat the same time to restoration,the capability of restoration of this model is better than ROF model and TBV_ROF model.
出处
《计算机仿真》
CSCD
北大核心
2015年第7期239-243,共5页
Computer Simulation
