基于最优小波和序列二次规划的信号压缩算法

为了寻找待压缩信号的最优小波,提出了一种适用于一维和二维信号的寻找其最优正交小波的算法.首先根据小波变换的多分辨分析原理,把待压缩信号投影在其小波变换子空间v-1和w-1上;然后令其在w-1上的投影达到最小并据此推出最优小波滤波器的推导公式;最后,基于序列二次规划求出给定信号的最优小波.实验清楚地显示了用新算法求出的最优小波的正确性,并表明用此算法得出的最优小波进行信号压缩,在压缩比不变的情况下,效果优于D-8小波等其他常见小波.

Signal Compression Based on Optimal Wavelet and SQP

To choose optimal wavelet for given compression signal, a new method to match 1D and 2D signals was proposed. In this method, the given signal was projected to its wavelet subspace based on the theory of multi-resolution decomposition. The projection was minimized and then the formula of optimal wavelet filter could be gained. In the end, the optimal wavelet for given system was calculated using SQP. Experiments show its validity. The results also indicate that signal compression with optimal wavelet has a better efficiency than with D-8 and other familiar wavelets under the same compressed proportion.