基于递推最小二乘自适应滤波算法的图像去噪

IMAGE DENOISING BASED ON RECURSIVE LEAST SQUARES ADAPTIVE FILTERING ALGORITHM

递推最小二乘RLS(Recursive of Least Square)算法是自适应滤波算法中的精确分析算法。它具有收敛速率快,精确度高等特点,但是发现目前RLS算法多用于对一维信号的去噪处理。使用递推最小二乘(RLS)算法对二维图像进行去噪,从处理一维信号变成处理二维图像信号,需要对RLS算法进行改进。先迭代得到滤波器参数,形成3×3滤波掩模,再改进算法对图像进行滤波;同时与常数比率维纳滤波和自相关函数的维纳滤波算法的去噪效果进行对比。结论证明在对图像进行较严重的模糊和加噪处理后,其他两种算法对图像的还原能力差,而递推最小二乘自适应滤波(RLS)算法具有优良的图像去噪性能。

Recursive least squares（ RLS） algorithm is an accurate analysis algorithm among adaptive filtering algorithms. It has the characteristics of fast convergence rate and high precision. But we find that current RLS algorithm is more used in removing the noise of one-dimension signals. Using recursive least squares algorithm for 2D image denoising,and converting the processing of one dimensional single to two dimensional image signal,there has the need to improve the RLS algorithm. First,we obtain filter parameters with iteration,and in turn form the 3 × 3 filter mask; then we improve the algorithm to filter the image; At the same time,we compare its denoising effect with that of the constant ratio Wiener filtering and the autocorrelation function Wiener filtering algorithm. The conclusion proves that after applying heavier blurring and noising treatment on the image,other two kinds of algorithms have poorer restoration ability on the image,and the recursive least squares adaptive filtering algorithm has good image denoising performance.