基于变分问题的区间双正交小波的图像去噪

采用非线性滤波方法处理图像去噪问题时,阈值参数的选取和恰当使用滤波器函数,对去噪图像的效果影响极大。文章构造了可用于非线性滤波算法的一族分段次小波阈值参数滤波器函数,它是Donoho的软阈值滤波器函数的推广,证明了滤波后的逼近是Besov空间中泛函的近似最小值。该滤波器函数次数越大,逼近效果越好,也证明了广义软阈值滤波器函数的极限是一理想低通滤波器。仿真结果证实了区间双正交小波比Daubech ies小波有更好的去噪效果。

Image denoising based on variational problem with interval biorthogonal wavelet

When images are denoised by means of nonlinear filtering algorithms,the selection of the threshold parameter and the proper filter function tend to have a great influence on the quality of the denoised images.A family of piecewise n degree filter functions of wavelet threshod parameter are constructed for nonlinear filtering algorithms,whicth are generalization of Donoho's soft thresholding filter function.It is proved that the filtered approximation is a near-minimizer of the function in Besov space.It is found that when the degree of the filter function gets bigger,the quality of approximation becomes better.It is proved that the limit value of the filter function is an ideal lowpass filter.Simulation results confirm that interval biorthogonal wavelets have a slightly better performance on noise removal than that of Daubechies's wavelet.