Q-shift复小波的一种新型构造方法及其在图像去噪中的应用

为了提高复小波变换的效率,本文提出了一种设计Q-shift复小波滤波器的新方法。与目前采用多相位矩阵的晶格分解结构得到正交小波的方法不同的是,这里从更为一般的完全重构滤波器组出发寻求满足特定要求的正交小波。不但可以构造出系数更为简单、运算更加方便的小波,而且可以实现任意精度的复小波变换。该方法的可拓展性好,可以很方便的添加如高阶消失矩等限制并简化设计过程。以普遍采用的Q-shift10/10小波为例,利用本文构造的正交小波可将复小波变换中的乘法运算降低到原来的1/3,而加法基本相当,且小波的频率选择性质更好。将其用于图像去噪的实验表明,采用本文构造的小波可以显著提高处理速度并得到更高的峰值信噪比(PSNR)。

The Design of Q-shift Complex Wavelet Transform and Its Application in Image Denoising

A new method for the design of Q-shift complex wavelet is proposed in this paper to improve the efficiency of complex wavelet transform. Different from the other methods which always generate wavelet filter from lattice structure of poly-phase matrix, we search the optimal Q-shift wavelet filter in more general restriction of perfect reconstruction. As a more general class of filters are considered, wavelets of less coefficients and more convenient for computation can be obtained. Furthermore, complex wavelet transform using our designed wavelets can achieve any required precision. Take 10/10 wavelet as an example, using our designed wavelet can reduce multiplication in complex wavelet transform to about 1/3 of the original, while addition operation remains unchanged. Further application in image denoising shows that, the processing is sped evidently and PSNR of the denoised images is also improved.