Optimization algorithm for 7/5-tap wavelet filters based on first order autoregression process

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 α 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 α values. Finally, took a as a central value to choose one set of values of free parameter α, and embedded them into the Jasper1.701.0 of the JPEG2000 standard to make an experiment for the image compression. The experimental results show that when the free lifting parameter α 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.