基于GCV准则的小波图像去噪方法研究

Generalized cross validation for wavelet de-noising based on GCV rule

小波软阈值去噪的关键在于阈值的选择。常用的阈值计算方法主要针对噪声信号为不相关的情况,并需要对噪声方差进行估计。对于含有未知噪声的信号,提出一种GCV准则确定阈值的小波去噪方法,并证明该方法得到的阈值是一种渐近最优解。该方法与常用的基于固定阈值和SURE阈值的去噪法进行比较,结果表明,无论是肉眼观察还是利用均方差和信噪比进行客观评价,基于GCV准则的小波去噪方法可以在噪声未知的情况下,有效的去除信号噪声,并很好的保留信号的原始特征。

Threshold is an important parameter in soft-threshold wavelet de-noising. Traditional methods for obtaining threshold assume uncorrelated noise and require estimating noise energy. For a signal containing unknown noises, the paper presents a method using generalized cross validation theorem to get optimal threshold (GCV-threshold), which minimizes the error of the result as compared to the unknown exact data. To verify the effectiveness of GCV-threshold,. a 1-D signal and an image are processed respectively by universal threshold of Donoho and Johnstone (DJ-threshold), Stein's unbiased risk estimator (SURE-threshold) and GCV-threshold. The simulation experiments show, whether by observation or by signal-to-noise ratio based on mean square error criterion as an objective quality measure, the de-noising results based on GCV-threshold are superior to others, which can reduce the unknown noise and retain signals' sharp features.