求解各向异性扩散LLT模型的新的图像去噪算法  

A New Image Denoising Algorithm for Anisotropic Diffusion LLT Model

作　　者：武婷婷[1] 顾广泽[1] 杨余飞[1] 

机构地区：[1]湖南大学数学与计量经济学院,湖南长沙410082

出　　处：《湖南大学学报（自然科学版）》2011年第8期67-70,共4页Journal of Hunan University:Natural Sciences

基　　金：国家自然科学基金资助项目(60835004;60872129;60572114);湖南省科技厅资助项目(2009SK3027);中央高校基本科研资助项目(531107040004)

摘　　要：基于四阶各向异性扩散的图像去噪LLT模型,提出了一种修正不动点迭代算法.该算法以最速下降方向为搜索方向,以避免直接计算逆矩阵,减小了舍入误差,提高了算法的收敛速度.利用矩阵的谱性质证明了该算法的收敛性.数值实验结果表明:对于256×256的'Lena'图像,在标准差为15的高斯白噪声情况下,本文提出的算法将信噪比由SNR=11.208 8提高到SNR=16.511 1.Based on the fourth-order anisotropic diffusion LLT model for image denoising, we have proposed a modified fixed point iterative algorithm. The proposed algorithm uses the steepest descent direction as the search direction in order to avoid computing directly the inverse matrices, thus reducing the roundoff error and improving the convergence rate. The convergence of the algorithm has been proved with the spectrum of matrix. Experiment results have illustrated that, for the ＂Lena＂ image which is corrupted with the noise of standard variance a= 15, the signal to noise ratio （SNR） by our algorithm is improved greatly from SNR=11. 208 8 to SNR=16. 511 1 .

关 键 词：图像处理 各向异性LLT模型 修正不动点迭代 

分 类 号：O241.82[理学—计算数学] TN911.73[理学—数学]