Abstract: A new image enhancement method based on Quad-tree Complex Wavelet Packet Transform（QCWPT） is presented according to the inter-scale correlation of the high frequency complex coefficient.The noisy image is decomposed into a low frequency approximation sub-image and some high frequency directional sub-images via the QCWPT，which both has shift invariance，good directional analysis ability，and has the ability to analyze the high frequency detail signal carefully.The complex coefficients in the low frequency approach sub-image are retained unchangeably，and the noise complex coefficients in the high frequency directional sub-images are removed by using of a non-Gaussian bivariate model according to the characteristic that the inter-scale correlation of signal complex coefficients is more stronger than it of noise complex coefficients.In high frequency directional sub-images，some complex coefficients correspond to the weak edges pixels are selected out and are enhanced，because their value are big in some directional sub-images but are small in the other directional sub-images.In numerical comparison with various methods ，the presented scheme has higher operational efficiency and outperforms the traditional Dual-tree Complex Wavelet Transform（DCWT），QCWPT and Wavelet Gaussian Scale Mixtures（WGSM） in terms of the PSNR index and visual effects.Experiments also show that the presented scheme can achieve an excellent balance between suppress noise effectively and preserve as many image details and edges as possible.

摘要： 提出了一种四树复小波包变换域层内层间系数相关性图像增强新方法。该方法利用四树复小波包变换具有移不变性、良好方向选择性和对高频信号的细致分析能力，把含噪图像分解成低频逼近子图和若干高频方向子图；在保留低频逼近子图复系数不变的同时，充分利用变换域信号复系数层间相关性强和噪声复系数层间相关性弱的特点，采用非高斯双变量模型对每一个方向子图复系数进行降噪处理。同时考虑图像的弱边缘在变换域某些方向子图内复系数值较大，而在其他方向子带内其值较小的特点，甄别出弱边缘点对应的复系数并进行增强处理。实验结果表明，无论是PSNR指标，还是在视觉效果上，该方法的增强性能均好于传统的双树复小波变换去噪、四树复小波包变换去噪和小波域高斯尺度混合模型去噪，在有效抑制噪声的同时，具有很好的图像弱边缘增强和细节保护能力。