基于一阶自回归过程的7/5小波滤波器优化算法

Optimization Algorithm for 7/5-Tap Wavelet Filters Based on First Order Autoregression Process

提出了一种基于一阶自回归过程的双正交7/5小波滤波器的优化算法.该算法首先由小波提升算法导出7/5小波滤波器簇系数和提升参数关于一个自由提升参数α的一维函数式.其次,以白噪声的一阶自回归过程作为输入图像模型,并采用满足完全重构条件的双通道7/5小波滤波器组进行子带编码,同时计算最大编码增益及其α值.最后,在所确定的α值附近选取一组值,并将每一个α值对应的7/5小波滤波器组的提升算法嵌入到JPEG2000标准的Jasper1.701.0中进行图像压缩实验.实验结果表明:采用优化算法的7/5小波滤波器,其系数和提升参数均为有理数,满足计算复杂度低、便于VLSI硬件实现的要求,特别是当α为0.08时,重构图像可以获得最大的峰值信噪比,此时的7/5小波滤波器为最优滤波器.

An optimization algorithm of the biorthogonal 7/5-tap wavelet filter for image compression was presented. Firstly, a one-dimension function of the 7/5-tap wavelet filter family coefficients and the lifting parameters with respect to a free lifting parameter a were derived from employing wavelet lifting scheme. Secondly, took first order autoregression process as an input image model, and using two-channel 7/5-tap wavelet filter bank which satisfied the perfect reconstruct condition to implement sub-band coding, and calculate the maximum values of the coding gain and corresponding free lifting parameter a values. Finally, took a as a central value to choose one set of values of free parameter a, and embedded them into the Jasperl. 701.0 of the JPEG2000 standard to make an experiment for the image compression. The experimental results show that when the free lifting parameter a equals to 0.08, the 7/5-tap wavelet filter can obtain the maximum values of the peak signal-to-noise ratio （PSNR） of the reconstructed image, and its coefficients and all lifting parameters are rational values, thus it not only reduces computational complexity but is also suitable for implementation via VLSI hardware, therefore it is an optimal 7/5 wavelet filter.