分数阶小波变换是小波变换时间-频域的分析方法在时间-分数阶频率域的推广，在时间和分数阶频率域具有表征信号特征的能力。本文在离散分数阶正交小波变换（DFRWT ）多分辨率分析（MRA ）理论基础上，推导出DFRWT系数分解及重构新形式并作二维扩展。根据图像DFRWT子带系数能量随不同阶数p变化的特点，提出基于DFRWT阈值降噪新方法。该方法在保持子带低频能量为绝对大值条件下，适当提高子带高频能量值，更利于抑制图像噪声。实验结果表明，与传统小波阈值降噪方法相比，该方法主观质量得到了明显增强，提高了峰值信噪比。%The fractional wavelet transform extend the analysis method of wavelet transform about time-frequency domain to time-fractional frequency domain ,can characterize signal features in time and fractional-frequency domain .Based on the theory of multiresolution analysis (MRA ) of the fractional wavelet ,the new forms about coefficient decomposition and reconstruction of dis-crete fractional wavelet transform (DFRWT ) are given and made two-dimensional expansion .According to the feature of subband coefficient energy of image based on DFRWT varies with different p order ,a novel image threshold denoising method based on DFRWT is proposed .The method in conditions of keeping the energy of low frequency subband for absolute great value ,appropriate to raise the distribution of energy percentage ,more beneficial for image noise suppression .The experimental results show that the performance of this method is better than the traditional wavelet threshold denoising method both in vision effect and peak signal to noise ratio .
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