基于正交小波变换的噪声下1/f类分形信号的恢复

Restoration of Noisy 1/f-Type Fractal Signal Based on Orthonormal Wavelet Transform

为了恢复噪声背景下的分数布朗运动 ,采用正交小波对混有噪声的分数布朗运动的增量进行分解 ,在线性最小方差估计准则的基础上估计出“细节”小波系数和“近似”小波系数 ,并重构离散分数高斯噪声 ,从而得到要提取的分数布朗运动。在仿真中 ,说明了“近似”小波系数对重构信号的重要性 ,并以恢复出的分数布朗运动的最小均方误差 mse和自相似参数的方均根误差 rms为指标说明了本文方法的有效性和优越性。

As one of the most typical models of 1/f-type fractal signal, fractal Brownian motion (FBM) has some unique characteristics. In order to filter noisy FBM, noisy DFGN is transformed based on the wavelet. The detailed coefficients and approximation coefficients are estimated by least variance rule, which are then used to reconstruct DFGN. Then FBM is estimated from the reconstructed DFGN. In the digital simulation, the mean square error ( mse ) of the restored FBM and root mean square error ( rms ) of estimated Hurst show the validity and the preponderance of the algorithm.