Brechet Laurent, Lucas Marie-Françoise, Doncarli Christian, Farina Dario
Center for Sensory-Motor Interaction (SMI), Department of Health Science and Technology, Aalborg University, DK-9220 Aalborg, Denmark.
IEEE Trans Biomed Eng. 2007 Dec;54(12):2186-92. doi: 10.1109/tbme.2007.896596.
We propose a novel scheme for signal compression based on the discrete wavelet packet transform (DWPT) decompositon. The mother wavelet and the basis of wavelet packets were optimized and the wavelet coefficients were encoded with a modified version of the embedded zerotree algorithm. This signal dependant compression scheme was designed by a two-step process. The first (internal optimization) was the best basis selection that was performed for a given mother wavelet. For this purpose, three additive cost functions were applied and compared. The second (external optimization) was the selection of the mother wavelet based on the minimal distortion of the decoded signal given a fixed compression ratio. The mother wavelet was parameterized in the multiresolution analysis framework by the scaling filter, which is sufficient to define the entire decomposition in the orthogonal case. The method was tested on two sets of ten electromyographic (EMG) and ten electrocardiographic (ECG) signals that were compressed with compression ratios in the range of 50%-90%. For 90% compression ratio of EMG (ECG) signals, the percent residual difference after compression decreased from (mean +/- SD) 48.6 +/- 9.9% (21.5 +/- 8.4%) with discrete wavelet transform (DWT) using the wavelet leading to poorest performance to 28.4 +/- 3.0% (6.7 +/- 1.9%) with DWPT, with optimal basis selection and wavelet optimization. In conclusion, best basis selection and optimization of the mother wavelet through parameterization led to substantial improvement of performance in signal compression with respect to DWT and randon selection of the mother wavelet. The method provides an adaptive approach for optimal signal representation for compression and can thus be applied to any type of biomedical signal.
我们提出了一种基于离散小波包变换（DWPT）分解的信号压缩新方案。对母小波和小波包基进行了优化，并使用嵌入式零树算法的改进版本对小波系数进行编码。这种依赖信号的压缩方案通过两步过程设计。第一步（内部优化）是针对给定母小波进行最佳基选择。为此，应用并比较了三个附加代价函数。第二步（外部优化）是在给定固定压缩率的情况下，基于解码信号的最小失真选择母小波。在多分辨率分析框架中，通过缩放滤波器对母小波进行参数化，这在正交情况下足以定义整个分解。该方法在两组信号上进行了测试，每组包含十个肌电图（EMG）信号和十个心电图（ECG）信号，压缩率范围为50% - 90%。对于EMG（ECG）信号90%的压缩率，压缩后残余差异百分比从使用性能最差小波的离散小波变换（DWT）时的（均值±标准差）48.6±9.9%（21.5±8.4%）降至使用DWPT并进行最佳基选择和小波优化时的28.4±3.0%（6.7±1.9%）。总之，通过参数化进行最佳基选择和母小波优化相对于DWT以及随机选择母小波在信号压缩性能上有显著提升。该方法为压缩的最佳信号表示提供了一种自适应方法，因此可应用于任何类型的生物医学信号。
