估计小波系数方差邻域大小的研究

利用小波变换去噪时小波系数方差的估计对去噪结果影响很大。自然图像小波分解后得到的系数在不同的分辨率中差异很大,所以利用邻域估计中心点方差时,不同分辨率应有不同大小的邻域。首先对在邻域中利用极大似然准则估计中心点方差进行分析,再结合自然图像小波分解后的系数在不同分辨率子带中,根据平稳性和重要性选择邻域的大小。最后进行去噪实验,并取得正交小波分解下理想的去噪性能。

Research on size of neighborhood to estimate the variance of wavelet coefficient

When the wavelet decomposition is used to denoise corrupted natural picture, the precision of variance estimation of wavelet coefficient has great influence on the denoising effect. Because the wavelet coefficients in different scales have quite different features, it is necessary to choose different window sizes in different scales to estimate the variance of coefficient in the window center. The outcome of variance estimation by maximal likelihood criterion is firstly analyzed. Then the variation and power of wavelet coefficient are also considered to determine the proper size of window in different scales. At last several simulations are performed to test the above analysis. The excellent simulated result shows the power of choosing proper window size in the specific scale.