基于四阶PDE模型的修正不动点图像复原方法研究

A Modified Fixed-point Iterative Algorithm for Image Restoration Using Fourth-order Model

图像在传输、扫描、显示等过程中,由于各种随机噪声的影响,导致图像质量下降。针对此问题,本文结合四阶模型和偏微分方程(PDE)提出了一种图像复原方法。首先分析了四阶PDE模型的不动点算法,为提高算法效率,基于各向同性扩散的LLT模型提出了一种不用计算逆矩阵的快速修正不动点算法;同时根据不等式的基本性质和矩阵的普性质,验证了所述算法的收敛性;最后,为验证该算法的有效性,进行了相关数值实验。实验结果表明:四阶模型中的高阶项可以避免图像复原中的阶梯效应,算法的执行效率较高,图像去噪效果比较理想。

The image quality decline will be caused by the effects of various kinds of random noise in the process of transmission,scanning,display and so on. In order to solve this problem,an image restoration method is put forward combined with the fourth-order model and the partial differential equation( PDE) in this paper. Firstly,the fixed-point algorithm based on fourth-order PDE model is analyzed and a fast modified fixed-point algorithm without calculating inverse matrix based on the isotropic diffusion LLT model is put forward to improve the efficiency of algorithm. At the same time the convergence of this described algorithm is verified according to the basic nature of inequality and general properties of the matrix. Finally,some related numerical experiments are carried on to verify the effectiveness of proposed algorithm. The experimental results show that the higher order term of fourth-order model can avoid the staircase effect of image restoration,the execution efficiency of this algorithm is higher and image denoising effect is ideal.